Don't worry about it, I think you'll understand really quickly. I think it depends on the subject of the sentence - either the subject can be "they" or "animals" (the meaning of both sentences is a little different):
"They are different animals." - "To jsou jiná zvířata." In this case, the subject is "they", so it doesn't matter if "animals" is a plural and neuter, in Czech you always use either "to je/to jsou" (single/plural), "to" it's just general demonstrative pronoun.
"The animals are different" - "Ta zvířata jsou jiná." In this case, the subject is "animals", so the definite article "ten/ta/to" for single masculine/feminine/neuter and "ti/ty/ta" for plural masculine animate/feminine or masculine inanimate/neuter must agree with the subject.
Thank you! In theory, I shouldn't have an issue with this, as it's similar-ish to other Slavic languages I've studied, but in practice... I think in part it's because there are so many demonstratives in Czech (at least, it certainly feels like a lot...) and trying to keep track of all those, I just managed to entirely ignore the jsou! (And I haven't got my brain around the plural nouns yet, either.)
It probably also doesn't help that my main focuses are two languages that don't use "to be" in the present tense, so I have this very bad habit of just forgetting that in most languages, it doesn't work to just leave a gap and assume that "to be" is understood 8-o
Firstly - there's no "one". Oni/ony/ona.
And "Oni jsou jiná zvířata"... Well grammatically it's correct but I just can't of a situation, where would I use it. Generally one would use "To jsou..."
I personally have the feeling that the phrase accuses some group of men of misbehaving. "jiný" would in this case have other (a bit of slang) meaning - big. And it would also be stressed. You know what, scratch that and just use "to jsou". And when you are a B2, come back, we'll talk. ;-)