Certainly a .22LR, .223/5.56mm, and .22-250 all fire a projectile that is roughly .22 .... but it's the size of the cases (and the amount of powder they hold) that makes all the difference. You can see this difference quantitatively with ballistics charts like the one linked below:
http://www.hornady.com/assets/files/bal ... charts.pdf" onclick="window.open(this.href);return false;
.22LR (not in chart) = approximately 1,000 to 1,500 feet per second and approximately 100 to 200 foot-pounds of energy
.223 = more than 3,000 fps and 1,000 ft. lbs. of energy
.22-250 = more than 3,500 fps and 1,500 ft. lbs. of energy
But I find the old ammo cartridge reference posters that you used to see in every Mom & Pop gun store were a great way to learn visually the relative differences of calibers. Easy to see with one look why a .22-250 is a more powerful round than a .223. It's hard to find these anymore even with some Google Foo ... but I have one saved, see below:
http://i850.photobucket.com/albums/ab70 ... _photo.jpg" onclick="window.open(this.href);return false;
As you'll see if you download the photo from above link and zoom in close enough to actually read the names of each cartridge, a .22-250 is a significantly larger overall cartridge than a .223 and thus packs more gun powder (not always the case, but usually works out that way).
I'm by no means a vetern or expert hunter (only been once) but I'm told that .223 is a borderline hunting round for deer (better hit them just right for a clean kill). But a .22-250 is probably enough for a Texas white tail. The .22-250 is meant more as a large varmint round, to hit hogs, coyotes, and other nuisance animals at a great distance. But can be used effectively on deer.
Then of course compare those two rounds to a "true" deer rifle round like a .243, .270, .30-06, .308 etc and you'll see the latter "deer calibers" are MUCH larger and fire a much larger/heavier projectile as well.
You'll find that many hunting rounds are much longer than military rifle rounds because military wants to keep the gun actions shorter (and thus lighter). The .308 is a perfect example of this "short action" vs. "long action" trade-off - it's basically a cut down .30-06 round so that it fits into short box magazines like the FAL, AR-10 etc, and also feeds into belt-fed machine guns. Weighs considerably less when carrying hundreds of rounds.
Of course, hunters aren't likely to carry 500 rounds of ammo. So long-action rounds are fine for them and pack more power.
But some "short action" military rounds like the .308/7.62x51mm are still good hunting rounds. As someone once told me when I was selecting the caliber for my deer rifle (.308), "a .308 will drop anything that moves on land in north America."
... I'm told the much larger rounds like the 7mm magnums and .300 magnums are almost overkill for most north American hunting situations unless you're shooting at large game at a great distance (something like moose or elk).
