It can be either, or both, or more.
For example, it could mean no dogs or cats.
It could mean no pets weighing more than 25 lbs.--so, essentially cats and small dogs are OK, but not larger dogs.
It could mean no dogs.
It could mean no dogs of certain breeds--Rottweiler, Doberman, Pit Bull, etc.
It could mean a numerical limitation, such as no more than 2 pets. (And any of the restrictions might apply to those 2 pets--breed, size, etc.)
You really have to ask about each specific place to find out what the restriction is.
Hope that helps.