How do I know if this cat is a stray?

So, just yesterday I found that there was a black cat with this gray chest that my cat has been 'hanging' with. Considering my cat is in heat right now and calling out to this cat, I assume it's her mate? She's got pregnant once with some cat last year, and I think it's the same cat. Anyways, how do I know if this male cat is a stray? I mean, I was able to get to my last step calmly and he trailed up to me and rubbed on my leg. I let it happen, and just went back in. I haven't been able to sneak a can of tuna out for him, but he wasn't hostile; and he didn't have a collar. His fur was all ragged and poofed. Yeah, I made the mistake with petting this cat whom I don't even know if it's a stray or not. But I quickly seized to wash my hands afterwards, for safety cautions. What should I do if this cat continues to roam around my house because of my cat? I mean, currently I have four cats in total; two kittens (male and female) and two adult females (one spayed, and one still needing to be spayed). Help?

I just took in a stray 13 year old cat. I called her Banoffee. I knew she was a stray as she was always outside, and sleeping in the car park. She was riddled with fleas (I showered her today and the water was a brownie red colour!), very underweight (usually a good sign they are stray), no name tag and no microchip. Her white fur was grey and dull with dirt, gooey eyes, full of a cold and very smelly. Now she shines!.
The cat will continue to hover around your house if your female cat is calling out to him. I had a cat a few years ago who brought in a male cat, he stayed around the house for quite sometime until he got his way! I get all my cats spayed and neutered now as there are too many cats being put down in rescue centres due to being over run. You could take him to the vets to see if he is microchipped, although most people don't bother getting their cats chipped, but apart from that, check the weight, if he looks ill and neglected. He won't go away until your cat is either spayed or stops calling out to him, or you keep your cat inside for awhile