Why does the military use different specs for their ammo than civilian ammo?

For your reading pleasure:
https://en.wikipedia.org/wiki/5.56%C3%9745mm_NATO

https://en.wikipedia.org/wiki/.223_Remington

Because military uses ammo that is used throughout NATO, not just in the U.S., and most of NATO uses the metric system, so its ammo sizes are designated in mm, not inches.

Why does the military use different specs for their ammo than civilian ammo?

The US Military, though backward in many other respects at least has a slight edge on the benighted general american population by having adopted the Metric System like those of us in the civilised world!
O.223 inches = 5.56 mm Same specification ! Duh!

There's no difference between the two. You just need to watch what you purchase.

Because the military is full of smug pricks