Until I started visiting this site, I didn't know that there was a difference between .223 and 5.56. Is there a difference? If so, does it matter? I own a bushmaster and I recently bought 1000 rounds of ammo from a gun show. Is it safe to shoot it out of my bushy?

Heres the technical explanation.  The M16/M16A1 fire 5.56mm M193 Ball ammunition using a 55 grain FMJ bullet, M193 Ball chambers the same as a .223 Remington.  When DoD went with the M16A2, NATO went along with it and the new NATO standard caliber SS109  aka as 5.56mm M885 Ball.  This uses a 62gr FMJ bullet with a hardened penetrator for armor-piercing qualities.  The chamber should be the same, and rifling rate for these (A2 is faster) is different, given that the 62gr bullet is significantly larger than the 55. The 55 gr bullet is stable in the M16A2 due to faster twist rate, but don't expect much accuracy firing the 62gr in an A1.

"An improved version of the M16A1 rifle it is replacing, the M16A2 incorporates improvements in sight, pistol grip, stock, and overall combat effectiveness. Accuracy is improved by incorporating an improved muzzle compensator, three-round burst control, and a heavier barrel, which can use the M855 improved NATO Standard SS 109 type 5.56mm ammunition, which is also fired by the M249 Squad Automatic Weapon."  http://www-acala1.ria.army.mil/LC/cs/csi/satoc.htm#M16A2