A Therapy Dog is a dog who goes into places to bring joy to other people such as patients in hospitals or nursing homes. Therapy Dogs are there for OTHER people and their sole purpose is to make people other than the handler happy. They often go into hospitals and visit the children's ward, or nursing homes to visit the residents there that were forced to leave their pets behind when moving into the nursing home. Therapy Dogs MUST be certified (usually through TDI - Therapy Dogs International) and must always ask permission from the establishment before entering the building.
An Emotional Support Animal is any animal that brings comfort to you (the handler) for minor disabilities such as anxiety or depression. They have no public access rights because they are not task trained. They are, however, granted access in rental housing and on airplanes with the note or prescription from a doctor or psychiatrist. And both places are allowed to ask to see the doctor's letter/prescription. The sole purpose of an Emotional Support Animal is to bring comfort and joy to its owner.
And a Service Animal is a dog or miniature horse that performs tasks for a person with a disability that couldn't otherwise easily do those tasks on their own without the help of the animal; comfort does not count as a task according to the Americans with Disabilities Act (the Federal Law regarding Service Animals). Service Animals are the only ones with public access rights in all places, but the person must have a documented disability such as mobility problems, PTSD, Seizures, Hearing Loss, Blindness, etc. Service Animals are allowed to be anywhere that the handler is allowed to be and the ONLY places that are allowed to ask to see the doctor's letter/prescription are the rental housing and airports. No business may ever ask to see those documents or ask what your disability is.
And just so you don't fall for their scams, any registration for Service Dogs or Emotional Support animals that you can find online are absolutely fake, money stealing scams. They have no legal bearing and you can literally register ANYTHING including a rock and a paperclip. (It's been done.) And the ADA doesn't recognize any registration anyway, so there's no need to ever pay for a piece of paper saying that your dog is "registered". There is on the other hand a training certificate (a piece of paper that you get from your trainer after the dog has completed training with them). That IS real. There's no "certification", but a training certificate is very real and can go in your documents along with your doctor's letter/prescription. I highly recommend keeping a log of all of the hours that you spent training your dog because that is your proof if you ever end up in court over your Service Dog, whether you're suing someone over a discrimination issue or someone is suing you for "abusing the system". I personally keep a composition book with me any time I'm training and I fill it out daily to keep a log of the hours that I've spent training each dog. But I also keep a copy on my computer just in case I ever lose the book.
I really hope that this helps you to understand and be able to explain the difference between Therapy Dogs, Emotional Support Animals, and Service Animals the next time you are faced with it in the future. Have a nice day, y'all!