Cats do care if you show them that you care about them. Yeah they have different personalities than dogs, but just because cats are generally more independent doesn't mean they don't care. I have a cat and I train her tricks. She comes up to me all the time, she sleeps with me, she asks for pets, and she really enjoys pleasing me with the tricks I taught her. But at times she can be independent. Like when she plays outside, she comes up to me and rubs dirt all over my pants saying "Hey I love you," but then she leaves to go chase a bird or claw at her tree then climb up it.
I also have dogs, they also care, but each dog has his own personality as well. They like to please me with their tricks, and if I'm sad my little dog comes up to me and tries to comfort me, whereas my big dog just continues eating his bone in peace. But if I'm scared then my big dog comes to protect me, (or at least try, I get scared over stupid things sometimes and I don't really need protecting.) But I'd have to say that if I needed protection and only my cat was there that she would help in any way she could, because she loves me. But I show her I love her by feeding, petting, teaching, and exercising her, just like what I do with my dogs. (Cat exercising is different from dog exercising, but it's essential for all species to get exercise.)