Use the word "military" when talking about a group of people organized for the purpose of attacking or defending from other countries or groups.
In the United States, men and women may serve in the military.
The military helps defend the nation.
There are U.S. military personnel serving in countries around the world. (personnel = people)
People who join the military can expect to receive training that might be valuable in finding a job later outside of the military.
In some situations, a military response is ordered when diplomacy fails.
Bob saw military action when he served in Afghanistan.
Jessica was involved in military action when she served in Iraq.
He serves in the military.
The word "militarily" is an adverb.
The United States is militarily stronger than any other country in the world.
Other countries are much weaker militarily.
The word "militant" can be used as a noun or as an adjective. In this case, "militant" can be used to refer to a person who takes a strong stance on an issue or is acting outside of the authority of a country.
Militants seized a warehouse full of ammunition.
A militant group formed a few months after the election results were announced.
Tammy’s militant position on the issue of abortion is a little unnerving.
Joe is very militant when it comes to disciplining his students.