evolution - Are domesticated animals really "more intelligent," or is that a myth/misunderstanding?

Often do I hear people speaking of how the domestic house cats are more friendly, less ferocious, less savage-like, and smarter and/or than their distinct but equivalent feline-species friends, like lions, tigers, jaguars, panthers, leopards, cheetahs, etc. Is this provably true in any form or way?

Are domesticated animals really "smarter" or less ferocious, or are some simply, but assumption of lessened threat potential, more so inclined to deem the house cat/dog as less ferocious simply because it's not such a big threat? Look at it this way:

This little beast here is "very cute" because he/she is small and barely 9 lbs. When playing, he/she isn't directly threatening to many human's safety, and many people are not afraid of cats; however, is he/she really smarter because he/she is safer and less dangerous to us humans only?

This beast, however, is hundreds of pounds heavier and many feet longer. Is it considered more savage-like because it can seriously harm and possibly kill humans by playing a little rough, which is like how a 9 lb. house cat would play equivalently, but would give you some light scratches at worst.

I've also heard arguments about "friendliness" of felines, usually claiming that house cats are friendlier due to evolution and nurturing/upbringing; lions/tigers, on the other hand, are claimed to be naturally unfriendly and have "more wild" in the, and incapable of being as "friendly" or "trustworthy" as a house cat. Point is, I'm probably not the only person who's heard this. Also, consider other animals, like dogs.

Dogs come from the grey wolf, to put it simply. Compare both a typical house dog and a wild grey wolf, and it's pretty obvious that many would assume the house dog is safer, friendlier, and less harmful, despite the fact that some domesticated dog breeds can pack a greater bite than the wild grey wolf.

Comparing the house dog's behavior to the wild grey wolf is also not a good measure of "friendliness", as compare a savage Homo sapiens from an uncivilized territory to a common city person, and you'd think the same thing: that the savage human is "less intelligent" and the city person is more so.