They really are.
Assistance dogs - which are not just guide dogs - must be trained to do physical tasks to assist the handler.
For example, mine tells me about my blood sugar levels, he also does deep pressure therapy if I have muscle spasms, and will (when I use a manual wheelchair) hold the weight of the chair briefly as I readjust hands on slopes/kerbs. He is worth his weight in gold as I can have symptomless hypos and I can go realllllllly high without feeling it too.
They do not have to be supplied by a charity, they do not have to wear a jacket either (though I think they should).
There is no such thing as public access right for 'therapy' dogs - these are dogs trained to do stuff, taken to hospitals, care homes, schools etc. As they do not have public access rights, theres no legal guidance on them wearing identifying jackets etc.
I would expect anyone seriously working an owner-trained assistance dog to know that assistance dog is the correct term, so them saying its a therapy dog would immediately raise red flags for me.
Assistance dogs should be well trained (and there are no protected rights to public access for trainee dogs!), however some of their training may not look like 'well trained dog' to the casual observer.
My dogs indication that my blood needs checking is to stand with paws on my knee and shove his face in my mouth and not get off no matter how much I protest, until I get my test kit out.
A friends dog practices trained disobedience - so if she asks her to go somewhere but the dog detects a problem (allergen in this case) the dog will refuse the cue and insist they turn around and leave via the nearest exit.
DPT looks like my dog is having a cuddle, though one would think its a bit clearer if hes lying on top of me and im on the floor, sometimes hes just laying up my body whilst i am reclined in my chair. He wont stop until the spasms fade though.
If you're in doubt - ask politely what tasks the dog is trained to do (not all, just examples). Not 'what conditions you have' mind.. just 'can you give me an example of the tasks your dog might do for you' - simply giving a person confidence to go out by being there is not a task!