These are excellent questions and today this post is going to answer both, as well as to explain a bit of the history behind ladies clothing sizing.
One of the most common misconceptions about vintage sizing - which, for the sake of this post, is going to focus primarily on the sizing applied to garments between the the years of approximately 1930 and 1960 - is that women in the past must have been a lot larger than your average woman today. This simply was not the case at all, and in fact, the average lady today is both taller and wider than than her mid-century counterpoint.
Then, as now, however, women come in all kinds of wonderful shapes and sizes, and there has been clothing designed to (ideally) fit them right off the rack. Ready made, as known as ready-to-wear, clothing, complete with sizes tags, emerged from the industrial revolution as factory began to churn out millions of mass market garments, thus freeing many people from having to choice between either making their own clothing at home or turning to a tailor or seamstress for their garments.
Whereas today's ladies clothing size scale starts as zero or two, depending on the brand, in the 1930s, 40s and 50s, most clothes intended for adult women started their sizing off at eight, ten or twelve, not zero (or, as has even emerged in recent years, “subzero” or “00” sizing).
There was no size zero for adults during this time period, and it is only as the decades have progressed and clothing manufactured gradually lowered the size number applied their garments (wherein keeping the actual measurements of the garments themselves about the same as they'd always been) that single digit clothing sizes became the norm for adult many women.
While there are no hard and fast rules (especially as clothing size numbers continue to drop as measurements remain the same - a practise which is known in the fashion industry as vanity sizing), generally speaking, garments from the 1930s-1950s are sized double plus or minus one or two sizes than what the same garment, manufactured and labelled by a company today, would be. For example, a dress from the 1950s with a size 18 tag would likely fit a woman today who wears a modern size eight or ten.
Case in point, when it comes to modern garments (produced in the last decade), I wear anything from a size a North American 3/4 to a size 8/9, with sizes four on top and six on the bottom being the most common (or, if working off of a small, medium, large, etc scale, an extra small to a large, with small and medium occurring most often in my closet).
With vintage garments from the 1940s and 50s, I typically wear a size 14, 16, or occasionally an 18 (with size 16 being the one which graces the most tags in my vintage wardrobe). Then, as now, even sized garments (12, 14, 16, etc) were more common, but some brands used uneven sizes (9, 11, 13, 15, and so on), especially those targeted towards, petite women, women who wore "half sizes", and plus sized ladies.
As there is almost no consistency between brands when it comes to sizing today (there was some variance in past, too, but not as much as nowadays), your best bet, without a doubt, is to disregard the size number on a vintage tag and instead work off of measurements (this particularly true if you're buying clothing online and thus can't try it on in person first before purchasing).
Believe me when I say that, regardless of if you wear vintage or modern clothing (or a mix of both), one of the best things you can ever do for yourself is to pay little to no attention to tag sizes when it comes to quickly judging if a garment will fit you or not. Such numbers are incredibly arbitrary and should never influence how a person feels about themselves either.
Instead of striving to be a certain size, channel your efforts in to finding garments that truly fit you properly. The best and most important way to do this is to know your measurements. I highly recommend that you periodically measure yourself at various key points on your body and keep a list of those measurements with you when shopping (back in December 2011 I detailed how to do just that in a post called The list of clothing measurements I never leave home without).

{Measurements are your best bet when it comes to ensuring that you find the best fitting vintage garment. Do not rely merely on size numbers listed on clothing tags. Image source.}
Any online vintage clothing seller worth their salt should always include key measurements in their listings. Generally, depending on the garment, these will include bust, waist, and hips. Other measurements may include overall length, shoulder to waist length, waist to hemline length, sleeve length, neck circumference, back width, and inseam. If you come across a garment online that doesn't include these measurements, but instead just a size number, be sure to ask the seller to provide details on the actual sizing.
Just as I might wear a vintage size 16 and a modern size six, so too am I different size in the 70s, 80s and sometimes even the 90s, as clothing sizes continued to change throughout those decades (for example, I have 1980s dresses that range in size from 4 to 12, with size ten being the most common for me).
Measurements are always what matter most. A label could say size 739, if it wanted to, and if it fit me comfortably and was flattering, I'd happily buy that garment. I do not put any stock into tag sizes and never let a bigger tag size determine how I feel about myself, so long as I'm presently happy with my weight (and even if, for whatever reason, I'm not, I still try not to let sizing bring me down at all).
Once you know your measurements, you'll likely figure out that there's a small range of one to three vintage sizes that work well for you (for example, if you're very svelte, you may wear a vintage size 8, 10 or 12, whereas most ladies will likely wear larger sizes, ranging from 12 to 22 or higher) and that you'll naturally gravitate towards these sizes (just as you would with modern sizes) when shopping for vintage clothes, whether online or in person.
Another point to keep in mind about vintage clothing sizes is that some companies produced different size ranges that were based off of different measurements. For example, throughout the mid-twentieth century, Sears often released the same garment in one or more of its most common size ranges: Juniors (designed for the slender teenage figure), Misses (average adult sizes), Half sizes (designed for women who were 5'3" and under and/or were of average height but fell between two even numbered clothing sizes), and Women's sizes (designed for plus sized gals).
For the most part, you really don't need to pay much attention to such terms, as they usually accompanied a size number as well. The one notable exception to this would be Women's sizes, which didn't progressively continue on from Misses sizes, as plus sizes do from smaller/average sizes today. Instead they often started at 38 and went up indefinitely from there (with 38 or 40 to 50 or 52 being a somewhat common size range). Again though, please don't worry about these numbers! You'll be using your own measurements when you shop for vintage garments and will simply be trying to find clothes that are as close as possible to those.
For those who may be curious, the following is a list - copied directly from the pages of a 1955 Sears catalog - that details the measurements, in inches, for the brand's Misses size range:
Size 10: 32.5 bust, 24.5 waist, 34 hips
Size 12: 34 bust, 25.5 waist, 36 hips
Size 14: 35.5 bust, 27 waist, 38 hips
Size 16: 37 bust, 28.5 waist, 40 hips
Size 18: 39 bust, 30.5 waist, 42 hips
Size 20: 41 bust, 32.5 waist, 44 hips
There is such an incredible variation in sizing between modern clothing manufacturers, that there's little use in showing you a similar size chart from one of today's brands. That isn't to say that each brand doesn't (in theory) stick to set of measurements across all of the garments they produce, many do, I just mean that this set of measurements is not shared universally between all clothing manufacturers. I suspect that just about everyone reading this post is familiar with how, when shopping for modern clothes, you can be one size in certain brand and a very different size in another (this is true almost no matter where in the world you buy your modern clothing from these days).
Vintage clothing sizes do not have to be a mystery at all, nor should someone ever feel deterred from wearing a vintage garment because the label says a size that it much bigger than the modern size they wear. One only has to hold up a size 16 dress from the 1950s to know that it's not a big garment in the slightest. In all likelihood, it will best fit a modern women who wears anything from a (North American) size four to a size eight or ten, depending on her personal measurements. But truly, there is no hard and fast rule when it comes to converting vintage sizes to modern ones or vice versa, and so once more, I must stress the importance of working off of your measurements.
These can certainly change over time to due to fluctuations in weight, but if you have a 38" bust today, you're likely going to fit into a garment with a 38" or 40" bust (assuming the seller measured the garment accurately), it's as simple, easy, and even fun as that. Once you know your measurements and have a decent idea of which vintage sizes fit you best, you can set about shopping for yesteryear clothing with much, much more easy and enjoyment.
Instead of flipping through a rack of garments that all have sizes such as 14, 16, 18, and 20 and thinking (erroneously) that they're all too big for you, you can instead (assuming one of those corresponds to your measurements) reach for your size and try it on in person, or buy it online (so long as the measurements stated in the listing will work for your body).
I may have touched on this point before in a past post, but it warrants bringing up again and is a very topical example to cap this post off with. It's often said that Marilyn Monroe, who was indeed famous for her va-va-voom curves, wore anything from a size 12 to 16. People often then rush to hold her up as a shinning beckon of plus sized beauty and body type because of this.
However, such folks are misguided because while Marilyn did in fact wear such sizes, they were vintage size 12s, 14s and 16s, not modern ones. If they were modern ones, she would fall into the lower end of the plus size scale, but again, they’re vintage sizes, which are equivalent to much smaller numbers today. As many of our own do, over the years Miss Monroe's weight fluctuated, but generally speaking, if she was alive (and the same size as she was back then) today, Marilyn would wear anything from a modern size 2 to a size 8 or even a 10, just depending on where she was buying her clothes.
By the same token, so too will your vintage size(s) differ from your modern ones. It would be virtually impossible for anyone who wears a size 16 in modern clothing to comfortably fit into a vintage size 16 and vice versa. You're not looking to match like to like, you're trying to find garments that fit you properly, and a list of your measurements is the key to making that happen.
So go out there, measurements in hand, and have a blast knowing that your vintage size is not the same as your modern one, and that such is exactly the same for everyone else on the planet! Fit, not size, is what truly counts, no matter if you're shopping for modern clothing or filling your wardrobe with nothing but vintage garments.