Training cats...
It obviously depends upon the cat (some dogs are harder to train than others, no difference to cats), but my experience...
You have to train them when they are young. Pretty much from being a kitten. I think it's very hard, possibly impossible, to change a cat's behaviour as an adult unless you have that framework in early on.
Cats are strongly food motivated. So training them around a reward mechanism seems to work the best. You can't really train them like dogs where they want to satisfy the owner. There is no point at all in training a cat negatively (same for dogs), they do not respond well to it, so for instance if they do something wrong like scratching the carpet, don't shout at them, just remove them from the situation and give them something else to do.
Cats are more equal with humans in the hierarchy. If you treat them well they will treat you well back. Dogs seem to be more unconditional in their love. I'm thinking that if you were homeless and didn't have enough food the dog stays by your side, the cat leaves
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Both our cats can 'beg' for food, respond to their name (return home), walk on a leash, one of ours can even 'high-five' you on command. Both know the sound of the 'laser toy' (my laser distance measure) down to the button press to turn it on. They don't scratch carpets or furniture - only their scratching posts.
Dogs are obviously infinitely more trainable but they are completely different creatures requiring daily stimulation and exercise. I quite like that our cats can get all of their stimulation from going outdoors every day. Though I know opinions differ on indoor vs outdoor cats.