To reiterate what
wilkeliza said... Service dogs, Therapy Dogs, and Emotional Support Animals (ESAs) are not interchangeable phrases, they do not refer to the same thing.
The Service Dog is the only one who is permitted public access and must perform at least 2 tasks to mitigate their handler's disability, and may also go through extensive PAT (Public Access Training) - depending on their trainer. There are owner trained dogs as well as dogs trained by service dog organizations. Tasks can be trained to mitigate both physical and psychiatric problems.
The Therapy Dog is the nice, calming dogs you see in hospitals, nursing homes, etc. They do NOT have general public access and are only permitted in places where they've been asked to come. They also do not perform any specific task for any type of disability. They do usually need to be certified through an organization such as TDI.
Emotional Support Animals do not have public access nor do they perform any certain tasks. They can be a calming presence for their handler. They can be allowed on flights and in no-pet housing with the authority of a doctor's note.
I personally have known several legitimate service dog handlers, one with an obvious physical disability, the other with a less obvious ("invisible") disability. Both went through painstaking amounts of training with their dogs, did enormous amounts of public access training - one girl's dog washed out (meaning after rigorous training, became apparent she wasn't meant for the work) and became her pet dog, and got another dog and did the training again and that dog became her service animal. She was always frustrated seeing people buying vests online, buying "certificates" online, then dragging their dogs into grocery stores and other places and watching their dogs piddle on the floor, snap at people, among other things -- all of these instances then made public access more difficult for her and her legitimate service dogs as businesses became more wary. This was someone who really needed and benefited from her dog's tasks, so it's very frustrating that so many people have no problems "cheating" by slapping a vest on their dog and then taking them everywhere. Not only that, but I'm sure many dogs become very stressed at the overwhelming stimuli of being in public all day because they aren't used to or trained for it. So they're not thinking about the well being of their pet, the well being of real service dog handlers, only thinking about themselves. A bummer.