Theatre and theater are spelled differently in American and British English.
In British English, “theatre” is standard.
In American English, “theater” is used.
AP style follows American English guidelines, so theater is the correct way to spell the noun.
This is also true for similar words, such as center or centre, meter or metre, liter or litre, saber or sabre, and fiber or fibre.
It’s important to choose one type of English and use it consistently. The QuillBot Grammar Checker can help you with this.