The definitions I have seen mean simply a person has served in the armed forces of the U.S. Charming has a good summary. A Vietnam veterans group I know of allows anyone who served in the military during the time of the Vietnam War, to be a member. A state I lived in allowed anyone who had ever served in the military to obtain Veteran's tags. Combat veterans served in a combat zone. You could certainly say that A. Neumann is a veteran of MAD magazine considering his 50 years of service there. Sorry, that picture always makes me half goofy.
A veteran is one who has served in the Armed Services. My sister doesn't consider someone a veteran if they haven't been in combat, but anyone who has served is a veteran. I am a veteran even though I did not serve in combat, though I did serve during a combat period. I was just stateside the whole time.
I've an answer to your first question only. A person who has served in the armed forces or An old soldier who has seen long service.