I recently read a blurb that slammed the use of 'rescue' to refer to rehomed birds. I probably agree with that POV, even though I also say 'rescue' (just because it's convenient).
A rescue is an animal is dire straights, who might not survive without an intervention. Typically you would NOT pay to rescue an animal.
If you pay for an animal, you have simply made a purchase. It is not technically a rescue.
So I suppose we should just use the term 'rehome' for older animals that we have purchased? Same goes for my two dogs that are from the SPCA...I have to stop calling them rescues. Neither one was in any danger.