I think you're missing the meaning in what people say. When they say Soldier, they mean anyone who's served, and are not singling out Sailors or Marines.
A soldier is someone who serves in a Military, be it Air, Ground, or Naval.
I do have to agree though that service men and women in the US don't get the recognition and respect that they deserve, in fact, they some times get the opposite of what they should be given.
I really do wish that people would realize that if they don't like War, they should take it out on the politicians that start them, and not the soldiers who fight them.