What’s the difference between 5.56 and 2.23?

I’ve noticed that most AR gear I’ve been looking at is chambered for 5.56mm NATO rounds… but when I’m at the range, most guys seem to be shooting .223 Remington ammunition.  Are they interchangeable?  I did a little digging online:

Apparently a barrel chambered for 5.56 NATO rounds can also shoot .223 Remington, but not vice versa.  Meaning, a barrel meant for .223 Rem. CANNOT shoot 5.56 ammo.  There are minor variations in the ammo that make .223 suitable to shoot in a 5.56 rifle.  My understanding is that you sacrifice a small amount of accuracy shooting a .223, but the difference should be negligible.

That said, I will probably buy some 5.56mm steel core for self defense purposes / zombie hunting… and use .223 to plink at the range.  My buddies @ CheaperThanDirt.com seem to have only a limited selection of 5.56 in comparison to .223 ammo.  Here’s a link to their full selection sorted by price lowest to highest: http://www.cheaperthandirt.com/ItemListing.aspx?sort=priceLow&pagesize=1000&catid=110

For specifics on the difference between 5.56mm NATO and .223 Rem physically, check out this PDF file for details:
http://www.ar15fornoobs.com/wp-content/uploads/223vs556.pdf (Source: http://ar15barrels.com)

Source: http://www.cheaperthandirt.com/MediaPages/ArticleDetail.aspx?mediaid=316