Theatre and theater are two spellings of the same noun.
Theatre is standard in British English.
Theater is standard in American English.
They’re both pronounced [thee-uh-ter], despite the difference in spelling. However, the pronunciation may vary slightly depending on regional dialect. For example, in American English, the final syllable may be pronounced with a “d” sound instead of a “t” sound: [thee-uh-der].
It’s important to choose one type of English and use it consistently. The QuillBot Grammar Checker can help you with this.