Generally speaking, active duty military must follow the same laws as civilians when carrying off-duty. If carrying on-duty (in uniform, with government issued weapon and under orders), they are under various military regs, federal rules and state rules. Most states have exemptions/allowances for on-duty carry, similar to those for police, varies by state.
If off-duty andyou do not live on post, you are pretty well prohibited from even transporting weapons onto base in your car (for example, when traveling to/from work),personal carry on base is essentially forbidden as well (this is due to military regs). They'll trust me with several hundred millions of dollars worth ofaircraft and hundreds of lives, but not with mygun. Sigh.
Some retail stores offer military discounts, but it's not a given.