Cats do wag their tails when happy, they also whip it when annoyed they can also whip it when excited or hunting tho the whipping motion differs in both
Cats wag their tails for an assortment of reasons. Pace and how hard they wag them can help translate reason. Excitement, contentment, irritation, playfulness to an extent, stimulated, etc. can all contribute to a cat wagging their tail.
I know a cat's tail have many minute canges, and slight back and forth moving akin to tiny waging at the end can be for happiness, the movement are however still very far of from the excessive wagging shown in dogs. So when differnt media sows what can only be decribed as dog wag for happy cat i'm peeved. (-_-;)
Honestly, so cute(^^), but pleassse do not show the girl being happy by making her tail wag. If a cat's tail is wagging the cat is angry, so many stories mixes that up and it's a personal pet peeve of mine (-_-;)