Dogs today are essentially a human creation, through genetic selection and breeding, not so much domesticated as, for all intents and purposes, created. And cats, by and large, aren't.
Perhaps there are differences in the degree in which humans have sculpted modern cats and dogs, but I don't see much fundamental difference.
There are ten times more dog breeds than cat breeds, almost entirely due to humans.
I'm trying to find for reference a recent study of cats' genome [※] that also mentioned how today's house cat is not much different genetically speaking from primitive feral cats, whereas as already said, plenty of dog breeds have never even existed in the past and are completely a product of human driven genetic selection.
( There ARE cat breeds also a product of human intervention, of course, but not in the numbers and variety of dog breeds. )
Edit : May as well add, human selection of dogs has altered them in fundamental ways. Selecting for co-habitation, so they don't attack farm animals, but protect them instead. Selecting for intelligence, so they can obey specific commands. Selecting for strength, so they can pull and carry. Etc. Most selection done with cats has been purely for aesthetic reasons, leaving behaviour aside.
[※] Edit 2 : https://www.sciencedaily.com/releases/2014/11/141110161042.h...
Yes, there are many differences between the domestication of cats and dogs, but not in any fundamental degree. Humans shaped these animals over time, albeit in different ways. The same is true for other forms of domestication, like cows, sheep, bananas, and wheat etc. Saying one is "smarter" than the other is silly. It's more that humans have selected and bread them for different traits.
The point is that the animals being compared, while considered 'similar' domestication wise, are anything but.