Theater vs. theatre
In most contexts, there is no difference in meaning between theater and theatre. Neither has any special definitions in general usage. The main thing that most English speakers and learners need to know is that theater is the preferred spelling in American English, and theatre is preferred virtually everywhere else.
Some Americans do make distinctions—for instance, that a theater is a venue while theatre is an art form, or that a theater is a movie theater while a theatre is a drama venue. There is nothing wrong with making these distinctions, but they are not consistently borne out in general usage. Even in 21st-century writing on the art of theater, the more American spelling now appears for all senses of the word.
The American preference for theater is a late-20th-century development (though the spelling itself is a centuries-old variant), so it is understandable that some people still resist it, and its newness means that exceptions are very easily found, but in this century the preference is entrenched. Searching a selection of 40 American news and cultural publications that put their content online, theaters appears 8,500 times from 2000 to the present, against just under 200 instances of theatres. This just suggests that theater is the preferred spelling for actual venues (the art form is a mass noun so would only rarely be pluralized), which no one seems to dispute. #Neo
Summary
What is correct spelling theater or theatre? In most contexts, there is no real difference between theater vs. theatre. What English writers and languages learners need to be aware of, however, are the dialectical differences between these spellings.
Different English speaking regions spell the word differently.
British English writers spell the word theatre.
American English writers spell the word theater. #neo
