In Russian, as in English, can this be a generic term for, e.g, lions and tigers, or does it just mean domestic cats that happen to be big?
It is a generic term for the taxonomic family as well. I don't think there is a language which can't call lions etc as Big Cats)
You may have come across this during the time between your comment and now, but the French language would actually say "grands félins" rather than "grands chats" :-)
Jokingly i entered, "more cats" and was marked wrong, but i want to understand why, and when to use <большое> and <ещё>
"More cats" would be «больше кошек».
Больше (with the first syllable accentuated) is a word in the Russian adverbial class, invariable, and means "more." You'll notice that it calls for the genitive case for the noun it operates on.
Большой / большая / большое (with the desinence accentuated) is an adjective that means "big," therefore it agrees in case and gender/number with the noun it operates on. To spice things up a little bit, больше can also be the comparative degree of this adjective: «Моя машина больше твоей.» = "My car is bigger than yours."
Ещё is another adverb that can mean "again," "still," "yet" or "even" depending on context:
- «ещё раз» = "one more time"
- «Он ещё не позвонил.» = "He hasn't called yet."
- «Я его ещё люблю.» = "I still love him."
- «У меня много, но я хочу ещё больше.» = "I have a lot, but I want even more."
- «Дай мне, пожалуйста, ещё чая.» = "Give me some more tea, please." (this is the only context I can think of where ещё alone would be translated as "more" in English.)
Does this phrase mean 'cats that are big' or 'animals from the cat family that are big'?
You seem to be asking the same question as me, but in slightly different words. ;) See the replies I've already received - it could be either. Might mean lions, tigers, leopards etc, or might just mean big domestic cats.