As far as I know British people "go to the theatre" meaning "go to see a stage play" but for Americans theater is a place where you can watch either a movie or a play. So would an American say "Would you like to see a play?" instead of "go to the theater?" Another question When someone says "Chicago is famous for theaters" how do I know if he's talking about live stage theater or a movie theater?
In the US, theater has two distinct meanings in this context
the legitimate theater, as distinguished from films, TV, etc. (often with the)
a place where plays, operas, films, etc. are presented; esp., a building or outdoor structure expressly designed for such presentations
When talking about seeing a live dramatic play (including musicals and comedies), it would be perfectly fine and common to say either
Would you like to see a play?
Would you like to go to the theater?
If you were talking about seeing a film, a person would most commonly say
- Would you like to see a movie?
- Would you like to see a film?
- Would you like to go to a movie?
- Would you like to go to the movies?
You might say would you like to go to the movie theater, but that would sound a bit stilted to most US ears.
The use of the term the theater, wiuthout more context, would almost always mean seeing a live dramatic performance.
The term theater is often used to refer to the venues where films and musical concerts are performed or displayed.
- What theater (or movie theater) is that film playing in?
- I'll pick up my tickets for the film at the theater
- The concert was held in the newly renovated theater
However, reference to going to the theater, without more, conveys the type of entertainment, a dramatic play, comedy or musical, not the building.
The statement, Chicago is famous for its theater [singular] would refer to the wealth of good dramatic presentations. Chicago is famous for its theaters [plural] would likely refer to the architecture where drama, film and concerts are performed, although some might interpret that to mean good drama.
Going to see a play is uncommon enough in the US that from my experience one person would say to the other, "Would you like to go and see |name of play|?"
It's not that theater-going is a rare occurence so much as it is a part of the infrastructure for seeing plays. As a rule, there are not theater districts in major cities. (Chicago and New York are obvious exceptions.) One does not go to the theater expecting to watch what is available... one goes to the theater with a foreknowledge of what will be there.
Otherwise, the phrases "would you like to go and see a play?" and "would you like to go and see a musical?" are the ones I would expect to hear from a friend.
I consulted the dictionary and learned that the word theatre is widely used for stage plays. In US, Australia and New Zealand, "theatre" is the usual word for cinema (but not always, right?). Cinema is strictly for films while theatre can refer also to cinema.
So the factors to consider would be:
- The context.
- The country/place you're in.
If you are not really sure and you cannot determine (given all the factors) if a person talks about live stage theatre or movie theatre, I think it will not hurt to ask him.