I would say every “special edition” version is a different film, but the 1981 release is not a different film just because a subtitle was added to the opening ruining the musical cue. It’s just a worse version of the same film.
I’m kind of indifferent to the ANH title being added, but the poor editing and the awful reformatting of the crawl itself means I can’t say it doesn’t hurt the film. I think it works better without ANH anyway. Since it is the first film, it seems reasonable for episodes to be ‘missing’ between SW and TESB.
In conversation I always call it Star Wars, and if someone wants me to clarify, I say “the first one” or “the original.”