Terminology:
-- service dog / assistance dog
-- service animal / service dog
-- emotional support animal / assistance animal
-- therapy dog
SERVICE DOGS are dogs that may or may not be wearing a service dog vest. Please don't interact, make eye contact with, or pet this dog while it is working. When in doubt, ask.
A service dog is a type of assistance dog specifically trained to help people who have disabilities including visual difficulties, hearing impairments, mental illness, seizures, diabetes, autism, and more. (source) Service dogs are highly trained to perform a specific function. Training can cost anywhere from $7,000 to $20,000. Properly trained service dogs are not reactionary animals and won't be distracted from their task by strangers. Many dogs don't make the grade because being a service dog is such an intense job; the standards are rigorous and very demanding. (source)
Service dogs are free to act normally when they are not working. Typically, the animals are taught to identify work versus free time by whether or not they are wearing their gear—if, in fact, they wear gear. Exceptions to this rule may exist, such as a seizure alert dog, which must not ignore an impending seizure even when it is not wearing its gear. Nevertheless, just as with any other trained animal, working dogs must still obey commands even when they are off-duty. Because of the strict behavior expected from a working dog when it is on duty, many owners will usually not permit people to pet the animal, or are reluctant to remove gear on request, such as for security inspections. (source)
Disabled owners of service dogs are protected under the Americans with Disabilities Act of 1990, which generally gives them the right to be accompanied by their service animal anywhere the general public is allowed. Additional federal laws protect people with disabilities partnered with service animals, as well as other types of assistance animals, from discrimination in housing the Fair Housing Amendments Act and on aircraft (the Air Carrier Access Act). (source)
The simplified version with list of major points to remember (read page). What businesses need to know about service dogs (read page). When is a service dog, not a service dog? (read page). Spotting fake credentials (read page).
Various organizations train dogs for service or assistance work. Call or email and verify.
Can Do Canines --- C.H.A.M.P. Assistance Dogs, Inc
Assistance Dogs for Living --- American Service Dog Association
Dogs 4 Diabetics, Inc --- Diabetic Alert Dog --- Support Dogs, Inc
Canine Partners for Life --- Liberty Assistance Dogs, Inc
Additional reading, the 'Service Dogs for Veterans / some for civilians as well' page published by a veteran.
SERVICE ANIMALS are animals that are individually trained to perform tasks for people with disabilities such as guiding people who are blind, alerting people who are deaf, pulling wheelchairs, alerting and protecting a person who is having a seizure, or performing other special tasks. Service animals are working animals, not pets. (source)
The Americans with Disabilities Act (ADA) prohibits requiring identification documents for a service animal (dog) and does not allow any questioning about specifics of a person’s disability. (source)
NOTE: while the ADA prohibits asking people about their disability, it does not prohibit asking about a dog's certification. And emotional support dogs are not covered under the ADA, so everyone has the right to question the owner. If in doubt, ask what work or task has the dog been trained to perform. If it is to provide emotional support versus aiding someone with a disablility, then they (the owner) are not entitled to accommodation. (source)
ADA requirements for service animals (read official page). The United States Department of Justice (DOJ) Civil Rights Division, provides information and technical assistance on the Americans with Disabilities Act (ADA). The DOJ changed the definition for service animal March 15, 2011.
EMOTIONAL support animal / assistance animal is not a pet. An emotional support animal is a companion animal that provides therapeutic benefit to an individual with a mental or psychiatric disability. The person seeking the emotional support animal must have a verifiable disability (the reason cannot just be a need for companionship). (source)
THERAPY DOGS are dogs that might be trained to provide affection and comfort to people in hospitals, retirement homes, nursing homes, schools, hospices, disaster areas, and to people with autism. Therapy dogs are usually not assistance or service dogs, but can be one or both with some organizations. (source)
The Disabled World website covers the subject very well. And read more here.