I recall someone who was into dog breeding who had a cut-out of a New Yorker cartoon -
Two ladies are talking at the dog show (dogs on leash) and one says to the other “Do you notice how they all seem to delight in not saying ‘female dog’?”
Not sure what the technical term is - but general usage on both sides of the pond nowadays sems to be the same, and my long perusal of Eglish literature does not bring to mind a different use; dogs are all dogs. “Bitch” is used to denote a female dog where the context and need is appropriate (or not).
The perjorative seems to have migrated from “you dog” or “you son of a dog” to a general comment about meanness in females.
Many things like that have changed over the years. We seem to see a lot of use of “chicken” as the generic for example, when we mean both sexes instead of poultry. “Rooster” only gets used when it’s required to be specific.
OTOH - language change - the camels in the opening of Ben Hur (the book) are referred to as “rude farting beasts”, not what might be considered the language of a classic nowadays. The word has become less genteel over the years?