I had the misfortune of having worked for about 5 years with someone who said he was a Viet Nam vet. He may have been but I and two more co workers who were vets agreed, he talked about it way too much. We never caught him in an obvious lie nor did we really try but there wasn't a single day that went by when he was not talking about being a war vet.
My vet co workers and I got so sick of hearing about it that we avoided him at every opportunity.
I don't talk about my service, not because I wish to avoid it but because it just never comes up in conversation, with one exception, every year on the Sunday nearest Veteran's Day, our Pastor at our little church (attendance about 60 on Sundays) has every vet come up and stand in front of the congregation and the congregation passes by and shakes their hands and gives out hugs. Even at that he doesn't distinguish between war vets and peace time vets. I like it that way, if you served, you served. If you weren't called on to go to a war zone, so what? You were there and ready, if called.
I like the idea that the pastor does not differentiate between wartime and peacetime vets, because the only difference is whether you were in the wrong place at the wrong time. I like the definition of a veteran I see once in a while as someone who at a point in their life wrote a blank check payable to the government for everything they had up to and including their life.