They had the draft. All 18 year-old males had to register for the draft, to be called up as needed. You could get a deferment if you were a full-time college student, but if that status changed, your name went to the top of the draft list, since you were a little bit older than the rest of the draft-eligible guys by that point.
At that point, you knew you were going to be drafted, and you could just go volunteer for one of the armed forces (for 4 years as opposed to 2) and at least have some choice in the matter, or you could just wait for the inevitable callup.
After you went on active duty, you were trained and sent off to your duty assignment. That could be service in Viet Nam, or anyplace else they wanted to send you. And you went where they sent you.
The reason you were in the service was because of Viet Nam, but Viet Nam was just one area of conflict in what we used to call the "Cold War", and at the time our military was involved all over the world, not just southeast Asia.
I hold guys who actually served in combat in Viet Nam with a special esteem, but I consider all who served honorably, performing their assignments faithfully, to be my brethren.
As I said before, you went where they sent you, you did your job, you sacrificed part of your youth for the good of your nation, and if everything worked out good you got grow old and join the Legion.
Brothers are brothers. We all just did our jobs, and we know those among us who we consider to be the true heroes.