Sevo:
There are two things you're confused about. The first is bullet diameter (typically called the "caliber"), and then the chamber cut into the barrel.
Let's start with .30 caliber bullets. Although referred to as .30 caliber, they are actually .308" in diameter. In metric, that's referred to as 7.62mm. Stranely enough, 7.62mm is not the same as 0.308", as 1in = 25.4mm, so a .308" diameter bullet is actually 7.82mm. The reason it's called 7.62mm is because in metric, they measure the diameter of the barrel at the lands, not the grooves. It's pretty confusing.
There are many bullets available in .308 caliber. all the way from 85gr to 240gr, maybe even heavier. Here are some examples of bullets that are all the same .308" diameter:

Now there are many different types of rifle calibers that accommodate .308" diameter bullets. Here we are talking about the shape of the brass case. The barrel has a CHAMBER cut into it to accommodate the particular shape of the brass case. This chamber restricts what you can shoot in the rifle. Here is a cross-sectional drawing of a rifle's chamber:

Two of the most common are .308 Winchester and .30-06. Take a look at this picture, and compare the .308 on the left, and the .30-06 on the right:

They both shoot the IDENTICAL diameter bullet, although you can easily see that you would never be able to shoot .30-06 in a .308 chambered rifle. You *might* be able to put a .308 in a .30-06 rifle, but the results might be catastrophic. Other common .30 caliber rifles are .30/30, .300 Winchester Magnum, .300 Savage, etc. There are a bunch.
Some of the more popular ones are also described by their metric equivalents. A .308 Winchester is called 7.62x51. A .30-06 is a 7.62x63. The first designates the bullet diameter, while the second number designates the length of the case in mm.
Furthermore, there are several 7.62 caliber cartridges that were developed by the Warsaw pact, like the 7.62x39 and 7.62x54R. Unlike their western counterparts, the actual bullet diameter of these is 0.311" to make things more confusing. Just like a .30-06, you could never shoot a 7.62x54R in a 7.62x39 or vice-versa. Bullet weights for com-bloc rifles are a little less varied. in 7.62x39, the most common bullet weight is 123 or 124gr, and in 7.62x54R it's 147 or 180gr.






Which one of the many calibers available for ARs you should buy depends on what YOU want the rifle to do. There are benefits/tradeoffs with virtually all of them, so first figure out what you want to do with the rifle, then pick the appropriate caliber.