A compound sentence joins two complete ideas.
The stand-alone test
I tightened the fitting. I went home. I tightened the fitting, and I went home.
Joined on purpose
Each side has a subject and a verb and can stand alone. Because I was late cannot stand alone — that is not this page.
I tightened the fitting and went home. — fine, shared subject
I tightened the fitting, and I went home. — two full clauses