At what stage does ‘that stray cat’ become ‘your cat’?

OK, so here’s the deal. The below pictured free-loader has been coming by my house for 4 years now. This is about the max distance you can get to him (presumed him because no kittens have been observed). If my door is left open, he’ll come in and snoop around a bit, maybe play w/ some catnip toys.

That little house you see in the background (yes its heated in the winter!) is where he can hang out in the rain or snow.

The cat (called ‘Outdoor Kitty’ or ‘OK’) gets fed (and as a consequence so do the raccoons and squirrels). After 4 and change years, we are now at a ~3m relationship, as long as I pretend not to see him. So, question (and poll below), do I now have 2 cats? At what stage is a stray cat your 2nd (or 3rd? 4th?) cat?

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