There isn't really a one-size-fits-all definition for a 7.62mm bullet. It depends on which one it is. Many firearm calibers are not designated by what they are exactly. For example, a .38 special and a .357 magnum fire the exact same diameter bullets. The .357 is the actually bore size in this example.
In general terms, a "7.62mm" bullet is a "30 caliber" bullet.
A .308 cartridge is sometimes called 7.62 x51 or 7.62 nato. The bullet diameter in this example is .308 inches.
A 30-06 cartridge also has a .308 inch diameter bullet.
A 30-30 cartridge also has a .308 inch diameter bullet.
In the case of most American "30 calibers" the bullets are .308.
When "7.62 mm" is used to describe Russian calibers, things are a little different. For example, 7.62 x 39 and 7.62 x 54 use bullets that are .310 inches in diameter.
In the above examples, there is .002 inches difference between the Russian and U.S. ammunition.
To make this more confusing, some guns made to shoot the Russian calibers above. For example a Ruger Mini 30 fires 7.62 x 39 cartridges ("Ak-47 ammo"), but has a bore for .308 bullets instead of .310. Some will say this can create excessive pressures, some will say it is just less than ideal for accuracy, but the fact is, almost all of the ammo available has bullets of .310 diameter. There are also cases where an American company may load cartridges originally designed for .310 bullets with .308 bullets. I believe the 7.62x39 soft points offered by Winchester are actually loaded with .308 bullets, but I may be wrong. If this is the case, firing them in most firearms in designed for 7.62x39 (AK's and SKS's, etc.) would still work, but might be less than ideal.
And it to make it more confusing yet, many Communist bloc rifles have bores of varying diameters. Some may be ideally matched with .308 bullets, .310 bullets, .311, etc. They only way to know for sure is to slug the barrel if one thinks it is worth the trouble.
Of course handloading overcomes all these issues.
There is commercially available 7.62 x54. I have heard Winchester offers some, but I have never seen it or seen it in their brochures. Norma makes brass cased, boxer primed 7.62x54, but it costs about $35 for a box of 20. Sellier and Bellot also makes 7.62x54 boxer primed brass cased soft points. It is reasonably priced (around $9 per box) and is reloadable. Wolf is considered commercial and is reasonably priced, but is steel cased like the surplus.
Concerning Surplus ammo, I've had very good luck with steel cased Czech "silver tip" ammo. It is found in light blue boxes with a a silver diagonal stripe on the side. The cases are greenish-gray in color and the tip of the bullet is painted silver. This silver tip doesn't designate it as being anything special like "armor piercing" or "sniper" ammo as some people trying to sell it might claim. I would recommend avoiding albanian made 7.62x54. It is probably the worst you can get. Some lots will work okay, and others will not. One of the main complaints about it is incosistent case dimensions. Some lots are very difficult to chamber is some rifles. It is easily identified by a brass case and it's head stamp. The two digits in the headstamp on one side of the rim indicate the year the other digit on the other side of the rim will be a "3".
One caution concerning surplus 7.62x54: Consider all of it corrosive and clean the rifle accordingly after shooting. Not too big of a deal, but it has to be cleaned after shooting and by a method appropriate for corrosive ammo. Some people selling surplus 7.62x54 will sometimes claim a certain type is "mildly corrosive. Don't treat this any differently than you would corrosive ammo. It is like the difference between being pregnant and mildly pregnant.
7.62x54 and 7.62x51 are NOT the same thing. 7.62x54 is a rimmed cartridge. 7.62x51 (aka as .308) is not.
7.62x54 may also be called 7.62x54R or 7.62 Russian (Sometimes 7.62x39 is also called 7.62 Russian)
7.62x54 IS the same thing as 7.62x53, a Finn designation you may encounter at some point.
Ballisticly, 7.62x54, 30-06, 8mm Mauser, .308 Winchester (7.62 Nato), and .303 British are all very similar. Of course this all depends on various loads, bullet weights, barrel lenght, etc. Handloading increases the possiblities.
I'm beginning to wonder if some of these folks actually know what they're talking about!
All I can say is, NEVER stop wondering. You will hear all kinds of BS concerning Surplus rifles and ammo.
I would suggest looking at
www.mosin-nagant.net
You will find a lot of information there.
I'm beginning to wonder if some of these folks actually know what they're talking about! 
