It depends on the animal and the situation they come from. Our first dog was a rescue. His male owner beat him and kicked him down a flight of stairs requiring him to have a pin in his leg. The wife gave the dog to a friend of my wife's and we ended up with him. Best dog I ever owned. Two years later we rescued a mix dog from a house that had no less than 40 animals living in deplorable conditions.
When the first dog passed we got another from the pound she was not a rescue, just an adoption. He had been surrendered to a pound due to allergies. She had a congenital heart condition and passed away in her sleep from a heart attack. 6 months later a woman from Church had to move into an apartment that didn't allow dogs so my wife brought home Cassie. Not a rescue.
The second dog we rescued (the mix) if now 14 years old. I wanted another female for her to train, so we went to the rescue sites. Long story short my wife fell in love with two male litter mates that were in a kill shelter. Instead of one small/ medium female. we ended up with two larger males that were literally two days from being put down. They have no puppy manner since they were separated from their mother at age 3 weeks but are responding well to obedience training and are eager to please.
This is just my opinion based on what I have seen over 15 years.
The language is so flowery and complicated today, every little deviation is creating a new set of words and formal categories.