No, Service dogs are seen as medical equipment and are only used to alert to medical issues. The other dogs that you mentioned are considered working dogs but are not service dogs and do not get any special rights compared to pet dogs. Even dogs used as ESA's aren't allowed in public places because they don't have the same level of training nor are as necessary as service dogs.
A service dog is one who is specially trained to help mitigate the effects of their handler's disability. That can include guiding a blind person, providing support and counter-balancing to someone with mobility problems, alerting to things like low blood sugar or irregular heart rhythms, and, and, and, and...... They are considered medical equipment, and have rights of access that other animals don't have.
SAR dogs are trained to find lost people. Their handlers may be active duty peace officers or fire fighters, or they may be civilians who work with local agencies.
Scent work dogs are either working detection dogs or sport dogs. Working detection dogs are trained to find things like drugs, explosives, insects, accelerants, electronic devices, and the like. Sport dogs typcally search for essential oils or their handler's scent.
A personal protection dog is just that, one trained to protect their handlers against things like kidnapping or robbery attempt. A dog capable of being a PP dog is usually not a good pet candidate. They are different from a bite sport dog.
Ok... I wasn't sure I knew that they were working dogs but I didn't know if the were considered a service animal or not. Ok well thank you just wanted to ask because I didn't know and I figured somebody else would.