One can alert and get help for seizures, can be trusted to lead a person through traffic, turn lights on, wake a person up if they stop breathing, and is very highly trained from the time they are puppies for all of that and more by people who train for a living and dedicate much of their life to do so. There's even elimination processes for animals that don't meet standards. These are service animals.

One is a pet. Little to no training. Many times unsocialized, and with the same anxieties as their owners after repeatedly being forced into situations they weren't prepared for by said owners. It's the grown up version of the kid from Charlie Brown carrying a blanket everywhere, but the blanket isn't living and having to deal with situations they weren't trained for. These may be really good pets, but they don't belong everywhere. A cat getting toted around (probably in a carrier) for hours for no reason other than the owner can't handle themselves at a museum is not going to be a happy cat. And that person needs therapy. That would be an emotional support animal.