Service dogs ARE service dogs. They are trained to perform a specific task
for those with disabilities. That disability may not be readily apparent (such as those trained to warn the person of abnormal diabetic levels or seizures, etc). Some service dogs are trained to perform specific tasks to assist a veteran through a PTSD episode - while that may sound similar to an emotional support dog, it is not. These service dogs are trained to lay on top of the vet until the episode passes or to actively disrupt the episode by barking or performing another specific task. They do not simply provid comfort to the vet.
"Comfort" or "Emotional support" dogs are NOT service dogs. They are not trained to perform a specific task for a person with a disability. There are laws that may provide for them, but they are NOT protected under the ADA. This is the most abused category - because any dog (or other pet) can provide "comfort" and "support" simply by being there.
Therapy dogs are NOT service dogs. They are NOT trained to perform a specific task to assist someone with a disability. They are provided access to hospitals, etc., through specific programs and/or agreements with the facility. They are NOT protected under the ADA.