Honor and honour are two spellings of the same noun or verb. The spelling depends on the type of English.
In American English, you use “we request the honor of your presence at our wedding.”
In British English, you use “we request the honour of your presence at our wedding.”
The same difference applies to similar words, such as “behavior or behaviour,” “labor or labour,” “favor or favour,” “favorite or favourite,” “color or colour,” and “humor or humour.”
It’s important to choose one and use it consistently. The QuillBot Grammar Checker can help you with this.