As much as we would like to think that we can take our pets anywhere with us, we know that that just isn't possible!!! So when you are traveling be sure to check ahead and make sure your pet is welcome. Though I do not think a brontosaurus would be welcome in many places, your cat or dog may well be.
A service animal is not a pet. Though they are part of your family, they are a working animal for the person who is handicapped in some way. This may be a physical or emotional handicap.
A therapy animal is a pet that is especially trained to go to hospitals, nursing homes, etc. with a specific handler to visit patients. They do not have any special privileges and are restricted to rules applying to pets and their owners.