The cat, when I am petting it, does a really deep, low pitched purr. Today it was walking all around me and doing that purr as was petting it. What does this purr mean?
Re the other one if chases lasers, does it know that I'm playing with it, or does it think it's really hunting (usually this cat doesn't like petting much)?
Aww, well of course the kitty knows you are playing but cats see playing very seriously. It's their training for the real world, when they will have to hunt to survive, fight other cats, etc...So to them, playing is very serious business...if it didn't know it was a game, then the kitty would not chase after a light or any toys, because they surely do realize that it's not something that can be eaten..
Oh yes, they know you're playing with them. One of our rescue cats dragged a long handled feather toy over to my boyfriend, dropped it at his feet, sat down and looked up at my BF as if to say, ok, make it jump around so I can CHASE it!!!!