We used to worry bout that too, but trust me, your chickens will know the difference, even if the dog in question is very similar to the one they know.But..... I worry that the birds will be inclined to not flee from canines as quickly as they should since they view ours as 'protectors'...will they know to be afraid if a stray roams through or will it be too late when they realize not every dog is like Mindy or Dillon?
Think about this. Chickens in flocks even large flocks like 100 birds, know their flock mates. In experiments when they were paired with a different bird but the same breed as their flock mates, they knew. So if they can differentiate between nearly identical birds, dogs shouldn't pose a problem.
Among our dogs are shelties some of whom are the same color and size as a fox. My husband used to worry the chickens wouldn't be afraid of foxes till the morning they all came screaming and flying towards the house. A fox was at the end of the yard. For a while we had a fox problem and the minute he poked his head anywhere they knew. For a while we let the guard dog stay with them.
This summer we got a new puppy. First we had him on leash while they were in their runs. Then off leash while they were in their runs. Then on leash when they were free ranging then within less than a week he was off leash when they were out. Perhaps because we and the other dogs were with him he was accepted pretty quickly. Initially he would go up to their runs and sniff and they would go right up to him, perhaps because I had treats in my hand for them.
He's pretty high energy and the birds, event the tiny bantams are fine with all our dogs.
If you have dogs that protect your chickens, lucky chickens. I would think your birds could tell the difference, perhaps even in the way a strange dog would act or carry himself.
I've also noticed if a stranger comes dressed like our usual attire, jeans, etc, the birds are wary but if we're with the person, they are quick to accept him or her. Someone dressed up they're more cautious about yet if my husband or I are wearing different types of clothes, it doesn't seem to bother them. Perhaps they have more innate intelligence than we give them credit for.