The "Vietnam Era" runs up to the time of the Mayaguez incident of May 12–15, 1975. It is generally considered to be the last official battle of the Vietnam war.
If a service member served at least 180 days on active duty prior to May 15, 1975, they are considered a Vietnam Era veteran.
To be an actual Vietnam veteran requires that you actually set foot in-country as far as I understand it. I don't know if there are any minimum time in-country requirements.
I am a Vietnam Era veteran, but not a Vietnam veteran, and would never claim to be one.
I will however, proudly claim to be a drunken-liberty-on-the-Gold Coast, New South Wales, Australia, veteran.