ESAs (emotional support animals) are not the same thing as service dogs[1]. There's debate about whether they're even effective[2].
Not only does this mean that people with ESAs likely don't need their dog as much as people with service dogs, it also means ESAs don't have the same legal protections. The only places that are required to accept ESAs are airplanes.
In any other context, only service dogs are protected.
1. From the article: "The [Americans with Disabilities Act] states, 'dogs whose sole function is to provide comfort or emotional support do not qualify as service animals under the ADA.'"
2. https://www.washingtonpost.com/news/animalia/wp/2017/07/02/t...