Therapy Animals differ from Service Animals in a few key areas.
Therapy Animal are screened and trained to be docile, allowing intrusions into their personal space that most animals will not allow. Therapy Animals are used in many different ways; comforting trauma victims, being a support to people testifying in trials, and visiting hospitals, are all some of the ways that Therapy Animals are used.
Service Animals are specifically trained to assist their Handlers. They are usually highly intelligent, and are trained to perform specific duties. A Mobility Service Animal may assist their Handler with transfering from a wheelchair or bed, open doors, flip light switches, steady their Handler's gait (ability to walk), and other tasks that may be difficult for their Handler to do on their own. A Hearing Service Animal is trained to alert their handler to sounds, which can be anything from traffic signals to doorbells. A Seeing Eye Dog is yet another type of Service Animal. They are trained to guide their Handler through a world that they can't see.
There are also Service Animals that are trained to alert their Handler to impending medical emergencies. Some are trianed for diabetics, others are trained for narcoleptics or epileptics. There are even Service Animals who are trained to recognise PTSD attacks.
All of these Service Animals provide assistance that enable their handlers to function in spaces that aren't designed for them.
Distracting a Service Animal could cause them to fail to perform their function. A Mobility Service Animal may shift their stance, causing their Handler to fall. A Hearing Animal could fail to alert their Handler to an oncoming vehicle. A Sight Animal could mistake the clearance in a hallway, causing their Handler to stumble and injure themselves.
Vest or not, obviously working or not... It's best to ignore the Service Animal entirely. Think of them as an extention of the person. If you wouldn't ask to stroke someone's bare leg... it's probably not appropriate to ask to pet their Service Animal.
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Sorry for the long post, but good information is always important.