What is the difference between a framing hammer and a claw hammer?
As others have said, a framing hammer is a specialty claw hammer. 

So what makes it different?  First, weight.  A framing hammer is typically 20-32 oz, compared with 10-16 oz for a "normal" household claw hammer.  That helps it pound large nails in only a few blows.  Related to that is the much longer handle on a framing hammer.

Second is the face of the head: it's waffled to prevent slipping off the nail head, helping prevent bent nails.  A regular claw hammer will sometimes have a textured face but not nearly as pronounced, and the face may also be smooth.  A regular claw hammer often also has a domed face to allow a skilled hand to sink a nail below the surface with minimal surface damage: that's a feature you won't see on a framing hammer.

Third, the claw is straight since it is optimized for prying boards apart.  A regular claw hammer is optimized for pulling nails.

If you're only building a garage, I'd recommend using your regular hammer rather than buying a framing hammer. (Or best of all, just go rent a nail gun!).  For inexperienced carpenters, the time spent hammering will probably not be what slows you down.  Also, the framing hammer is tiring enough that after a couple hours you may actually be faster with a smaller, regular claw hammer.

If you do get a framing hammer I recommend a lighter one.  You'll work faster when you use it, you won't lose much power over a heavier hammer, and you'll feel much better on the second day.  In 2010 if you hammer enough that a 32oz hammer makes a difference versus a 24oz hammer, you have a nail gun anyhow.