With our two cats, they definitely respond to different things... One has a bigger vocabulary of words he understands, but he only complies with what we want if he feels like it, or if it will get him a treat. If I really need him to be out of trouble/danger, I just scoop him up and move him, and he might complain, but there's no sense punishing him when he doesn't understand that he's doing something *bad*. He's a bit spoiled now because he's sixteen years old, and so we pamper him a bit more and are more lenient about his misbehaviors...
Our younger cat, if I see him having an idea that I don't want him to go through with-- usually stealing his brother's food-- I just go and stand between him and the thing I don't want him to have/mess with, and he understands that he's being herded (before we took him home, he was fostered by a shepherd dog for a brief time, between being old enough for his cat!mom to wean him and our being able to pick him up and take him home from the rescue farm).
I use the words they know a lot, when talking to them-- Our older cat knows WAY too many food-related words, as well as a few outside-related words, and 'spaceship' (his favorite toy). Momo, my baby, just likes to be talked to whether or not he understands any of it, so I talk to him a lot about nothing in particular when I'm home alone with the cats, or if my talking to him isn't an interruption for anyone else in the room. He enjoys the attention and seems to feel like things must be all right if I'm talking to him in a calm, happy tone, and he's a bit of a worrier so I like to make him feel safe and relaxed.
As far as non-verbal communication, I'll give Lego (our old man) a stare-down if he's doing something he knows we don't like but that isn't immediately dangerous, like jumping up on the kitchen counters but not going near the stove. He might just stare right back, but sometimes he gets the message and defers to me as the higher authority between us. I pet them both and know which their favorite spots for scritches are, and whether a belly rub or play is desired (which is mostly just my reading their communication to me), and I return face-rubs (though I have to take my glasses off in order to rub my face against either Mo's face or Lego's shoulder-- he's not so much a face-to-face guy). Gentle headbutts, because that's affection they understand perfectly (Momo is a big fan of just smushing his face into me, in particular).
They both sometimes like to have their faces held-- as in, I cup my hand and an entire cat face just fits into said hand.
With Lego, I sometimes let him 'steer' me-- I'll pick him up in my arms and he'll just lean slightly and tighten his paw around my arm to communicate to me where he would like me to carry him.
And of course I'll pat my lap or the arm of a chair to let them know they're free to come up and sit with me-- sometimes Momo likes to ask permission before jumping up, either by pawing at the side of the chair, or by a particular meow. They have some different sounds that they make, though Momo is more of a warbler, and Lego has distinct words he uses specifically for 'feed me' or 'outside!', or 'FIX WHAT I'M UPSET ABOUT', as well as a 'hello' and a 'goodnight'.