[header] How to know if a cat is a stray [title] See if the cat approaches you. [step] A cat's behavior towards people can be a big indicator of whether or not a cat is a stray. Since stray cats have once been socialized, meaning they've been around people and most likely lived in a home, they are often not as skittish as feral cats. 
Stand or sit near the cat and see if it approaches you on its own. If it does, it is probably a stray that is lost.