A therapy dog is not a type of service dog.
Therapy dogs are trained, certified, and insured by a therapy dog program. They visit institutions such as hospitals, schools, and nursing homes, only when invited, for the purposes of cheering up or educating people in those institutions.
A person with a therapy dog has no right to demand access to places where pets are not generally permitted, or to have pet fees, such as deposits, waived.
Some therapy dog programs include:
The Delta Society
Therapy Dogs International (TDI)
Therapy Dogs, Inc.