Can cats tell that you understand them?

I just wanted to know if I was imagening things? 1 or 2 things have made me think my 2 do.
The first thing that made me think this was, when Creep was in pain and she was aking for my help. When I told her I was going to take her to the vet to make her better, She seemed more happier when I told her. She was even more happy when I took her to the vet to have the treatment she needed.
The second time was just afew minutes ago I was asking about Quicksilver in another part of this forum. When I told her I was going to take her to the vet to be spayed, she been alot calmer and she is sleeping on me as I write this.
So is this just coincidence or do cats know that you are helping them, when you tell them?

I think they understand. They also know things intuitively. My husband travels a lot and his cat always knows when he is coming home. Oberon will go outside and wait by the front gate for him, sometimes for hours, but always on the day he's coming back!

Cheers, from
SwampWitch

Just last night I asked Wickett where his blue mouse was. He loses the things in minutes. About 5 minutes later he came trotting down the stairs blue mouse in mouth. Might have been a fluke but I wonder. I tried asking him where Frankie's pink mouse was but I guess he didn't know.