What's the legal difference between an emotional support dog and a service dog under the ADA? Two things: the dog must be public access ready and it must be TRAINED to do some service specific to its handler's disability. Training your dog to do something specific to your disability is the easy part.
Getting your dog public-access ready is a big deal. Failure in this area is the most common reason that professional service dog training programs release so many dogs for adoption as pets. The best trainer in the world can't train the average dog to be comfortable, peaceful, and focused on its handler while being out in the crazy human world full-time. A great companion dog often is not capable of becoming a service dog. Having a dog to accompany you everywhere if it does not have the right temperament, socialization, and training is highly stressful to the dog (and the handler) and is abusive. The Psychiatric Service Dog Association has a good page with details of what one has to do to help a dog become ready for a life of service.
However, let's assume you have a dog who is trained and ready for public access. What else do you have to do to meet the legal definition of "service dog" under the ADA? The dog needs to be trained to do one or more things specific to your disability. Like what? Check Maeve's short list on her pros and cons page for some examples. The Psychiatric Service Dog Association has a longer list . Note: just being a calming presence or being soothing to pet doesn't count as a trained behavior.