I think of a “rescue” animal as one being from a pound, but I understand that logically, the term should and does encompass more than that.
I have two cats that were kittens born to a mother who was living at a muffler place in The Bronx. The mother kept having kittens and I went with a friend and the owner let us take two. They were dirty and one had ringworm but after lots of money on vet bills, they were fine and healthy. I don’t consider those “rescue” animals but they were rescued.
My third cat was a stray on school property – a big wooded area where I saw a coyote once and there are bears, too, so he’s a tough cat who lived there at least five years that I know of. He was neutered previously so he was owned by someone, possibly someone who dumped him in the woods, or he ran away. I don’t consider him a “rescue” but I rescued him.
I personally don’t use the term “rescue” animal. I describe where I got my cats or I will say a friend’s dog was from the shelter. People can infer what they want. I’m not opposed to the term, I just don’t use it.