I know this may be dumb, but i dont know.. and i am building a rifle and need to know which to get... if they are different.

Basically, yes. The 5.56 though has a thicker shell walls because it produces higher velocities.

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Beat me to it

As a general rule, if you have a choice between .223 and 5.56mm chamber, most people (and most applications) are served better by the 5.56mm

5.56mm is a military load. it produces higher volicity and pressure
.223 is a comercal load with lower volicity and pressure
like DK-Prof said most applications are served better with a 5.56mm chamber. however if you are looking for long range accuracy you should go with something like a .223 because most of the match grade rounds are loaded to .223 specs and  you will not get the same accuracy out of the 5.56mm