I may say words of greeting, but I don't expect animals to understand a large vocabulary any more than I expect to understand other languages myself. Humans chatter, and pets learn to understand tone of voice, etc the same as we do. (If someone asks how you are, and you reply "Fairly suicidal, thanks" in a happy, singsong voice, they won't notice the middle word.) We don't understand the things that cats, foxes, and ravens say to each other, although they have dozens of "words." We don't even know what they might want to say in most cases.
It makes me very sad when I meet a dog whose owner only talks but never listens, and has no other dogs to play with. They get so discouraged that they even loose their own body language. A dog's "follow me" signal is very clear, and has led to many rescues, but most people don't even see it.
When a dog jumps up at me, I think it is most interested in smelling my breath most of the time as part of a greeting, so I bend over and/or sit if I want to be polite. I'd like to have a pet, but I can't feed one without starving a wild animal at the other end of the supply chain, and I value nature more. I considered collecting road kill, but then I spotted a very rare wildcat subsisting on it.
My friend once had a dog who would chase deer into the water, so that they both could eat, and share. That dog knew darn well that he was a full member of the group. Once, when there was a mix-up, he even managed to hitch hike home. He snuck into the pub, and by the sixth round, was sitting up happily on a bench along the wall, surveying the scene. My friend asked the waiter if there was a problem, and was told the dog was the best behaved one of the group. Words were not needed.