Please explain the difference between an ESA and a pet.

I have had many pets over the years and they all provided me with some level of emotional support. I understand that a service animal is trained to do specific things, like a guide dog for the blind and can be in places where animals normally can't go. Is the concept of an ESA really just a way for people who are really attached to their pets to take them places where a pet is not permitted or am I missing something?