For reloading purposes, 5.56mm and .223 Rem cases are exactly the same thing except for the headstamps. There is no differance whatsoever like the examples you named..
Nobody makes reloading dies specific to the 5.56MM, except the military arsenals perhaps.
The differance is in the chamber dimensions of the rifles.
The 5.56 chamber is very slightly looser then the .223, with a much longer leade or free-bore for long tracer bullets, combat dirt, etc.
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