Cats are very much like children also. I read in a website on cat anatomy that this is because the limbic system in cats (emotions) is very similar to humans. They have less frontal lobes however, but still seem to be able to plan in a minor way.
Predators have to plan to catch things to eat.

Our cats when young, before one year old, respond and learn just like a baby does. They show delight when doing a new thing, and look for reinforcement for their successes--loving praise. Our Houdini, in fact when he wants my attention taps me with a soft paw on the hand or leg. I've seen him tap both of our other cats this way, as an invitation to play. He will also tap a bare foot. He leaves presents... a special toy in Weezie's bed, a special toy in Oreo's bed, and a disc for me to put in his shooter to leap for. He once brought me a toy and dropped it in my lap when I woke up one morning. Just like a dog!
All our cats know "all done" as a sign that something is over, or a treat is gone, or they are leaving the vet. They visibly react to "all done". Weezie still fetches, and Houdini fetches 1 in 5 throws now. I have a large basket with all their toys in it..and a Xmas stocking I've not delved into. The other day both Houdini and Weez were sorting out things they wanted to play with. It was funny to watch. They also go thru our to be washed laundry basket with great pleasure! We leave it on the upstairs landing to be added to for the wash, and they love to play in it!

Weezie still has some baby characteristics and I think they will be more or less permanent...but Oreo being much older does not. But she is still like a child, afraid of thunder or firecrackers, and the garbage truck. Oreo makes a special meow for OUT...
ooooouuuuuu....and sits by the door. Not a meow, not a cry, and not a moan. All that is missing is the "T". She does this in her cage going to the vet too. Sheba used to say "ma" for me.

Cats and dogs are very smart, if we listen to them and watch their body language. A nod of my head in a certain direction, and ours will follow.

I think the differences are in neediness, and clinging type behaviors. Cats do not display this much at all. While they will be close to you as company, they do not "beg" for attention unless hungry (or wanting play when kittens). Cats do not like a dominant human, and prefer quiet type interactions. They will do wonderful things, if they want to please you though.

Since I retired, I am enjoying our cats much more. I really noticed much less, when I was working so many long hours!
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While Oreo is afraid of big trucks, she loves them when they are NOT moving. The past road work the city did down in front... is a case in point. Here is a photo of her conquering the digger!
She visited ALL the machines over the few months this project was active! LOL