What one calls "going to see a motion picture in a movie theatre":
Going to a....
I would have guessed that the designation used would have depended on where one lived -- a regional thing.
Recently I watched an interview with filmmaker Richard Linklater. He made a point to say: "... not, going to 'the movies', but 'the show'." That is how my film-going buddies and I referred to seeing a motion picture at the Terra or Astral theatre.
CFB Borden, Ontario, and "a small town in Texas" are many miles apart but, in the 1970s at least, young denizens of those two towns shared a particular term.