It is indeed different. The most straightforward role of a "patient" is the object most directly and strongly changed by the action of the verb. However, languages use "direct objects" for more than just that. For example, reading a book or hearing a sound only slightly affects the book and does not has any influence on the sound. And still, languages as different as English and Japanese treat their verbs for "hear", "see" and "read" as acting directly on these objects.
However, we start with a few simple verbs like "see", "read", "write", "want", "cook" and "love", which grammatically work the same in Russian and in English.
Given that you are far into your tree, you might have noticed that the verb "to listen" is not transitive in English (you listen to somenthing) but is transitive in Russian. As for "like", the Russian equivalent is more similar to the English "to seem", whereas in English the verb "like" is no different from "want" or "love".
The word is котёнок. The words for kitten, puppy, piglet, calf, fox cub, bear cub, wolf cub, baby duck, chicken, fawn, foal are «котёнок», «щенок», «телёнок», «поросёнок»,«лисёнок», «медвежонок», «волчонок», «утёнок», «цыплёнок», «оленёнок»,«жеребёнок» respectively. I hope you can spot the odd one out. Everything else behaves the same, and also ends in -ята in plural (sg. котёнок → pl. котята), which is a remnant of the time -ёнок was not really there.
Actually you can say "I want cat" if you are asking for cat meat off a menu. It would be the same if you are buying a fur coat and wanted the fur to be from a lynx cat. When you say "I want fish" you are asking for a non specific amount of fish in general. Not 1 specific fish. If you are asking for 1 specific fish in a pet store, you would say "I want that fish" or you could point at the one you want and say "I want the fish" or even "I want a fish". This is the way English is. We use prepositions a lot and which preposition we use (or don't use) changes the meaning of the sentence.
I am inputing кошку and it continues to tell me that I am incorrect because the answer is кошку. The question is multiple choice and I have cycled through all of them hoping that the bug would resolve itself but to no avail. I’ve reported it, I’m just saying something here so that the problem is more visible for the mods.