Under the Americans with Disabilities Act (ADA), service dogs are defined as animals that are individually trained to work with people with disabilities to perform specific tasks for them. As such, service dogs maintain full public access rights. They are allowed in all housing, airplanes, public transport, etc. A service animal certification will guarantee the owner these rights and more.
Emotional support animals, however, are not classified under the service animal umbrella according to the ADA. They are not trained for specific tasks to aid their owners unless the owner decides they should be, which is what sets them apart from service animals.
They do still provide support and are recommended by doctors and mental health professionals, but they have a more limited set of rights. Emotional support animals don’t have the same access to public spaces, but ESA forms will guarantee them entrance into housing.