The difference between the two animals and the various words used for them are much less clearly defined in English.
Hare is the oldest word and was used for both. Rabbit was borrowed from the continent, where it had refered to rabbits and seals. Coney comes from Latin cuniculus via French, and it's cognates in other Romance languages refer to various types of rabbits and hares. Bun/bunny was a Scottish word used for small rabbits and squirrels. Jack-rabbit means a hare. Swamp-hare means a rabbit.
It's safe to say that even if you take great care which word you use when you translate from Ukrainian, more than half of English speakers will probably not pick up on that subtlety.