I just discovered the undefined tag "compatibility". I'm of the mind that it is quite similar, and potentially better than the more unwieldy "introducing-pets".
I think they should be synonyms and transformed into "compatibility".
The way I see it. Before you get a new pet, you'll want to make sure it's going to be compatible with the ones you already have. I see it being used more with fish, making sure all the fish in the tank are compatible with each other.
Introducing pets, is when you bring the pet home. It's different in the sense that it's about the transitioning process; making it as stress free as possible. Two cats are going to be compatible, but you'll want to know how to introduce them properly so they don't fight with each other if you can help it.