In terms of VA benefits, a lot of people are confused by this question. It is confusing because a reservist can be a veteran, and a veteran can be a reservist. However, a reservist doesn't have to be a veteran.
A reservist is someone who has served in the National Guard or reserves of a military branch. A veteran, on the other hand, is someone who has served on active duty in one of the military branches. To be eligible for VA benefits, both reservists and veterans must be discharged under anything besides dishonorable.
This is still a little more complicated than a yes or no answer, so let's talk about it.
Every single branch of the military has its own reserves. When you join the reserves, you complete basic training and military school and then you go back to your civilian life. At this point, since you're not considered to be active duty, you're not considered a veteran. If the President or Secretary of Defense requires additional military support, then the people in the reserves will be pulled to active duty and their service will count towards VA benefits. Those reservists can call themselves veterans as long as they are discharged with anything besides dishonorable.
The National Guard is similar to the reserves, except the National Guard is controlled by the state, and the federal government controls the reserves. People in the National Guard also attend basic training and full-time military school. They're on duty one weekend per month. If someone on the National Guard is called to active duty by the state, it doesn't count towards their VA benefits. However, if the federal government calls the National Guard for active duty, it does count towards VA benefits.
Unfortunately, this question is hard to answer with a yes or no. If you are confused about your veteran status, the best way to figure it out is by reviewing your military history. No matter what, a period of active-duty status is required to be considered a veteran.