Translation:A turtle and a rabbit
If you look up 'hare' in Korean-English dictionary (Naver) you get "토끼". So I doubt Korean distinguishes the two in ordinary speech.
Most English speakers can't distinguish a hare from other rabbits either, at least in my experience. Biologically, hares are one type of rabbit (precocial, born with eyes open and fur so not really needing burrows). It looks like the word 토끼 might even extend to all lagomorphs, including pikas, though probably not in common use:
hare = 산토끼 ("mountain rabbit" -- in Japanese, "wild" rabbit, but mountain means wild in Japanese too and is used in other animals' names, say wolves or goats)
pika = 우는토끼 ("crying rabbit" -- they live wild in North- but not South- Korea, in the mountains. An indicator species of global warming -- all lagomorphs are very temperature-sensitive)
As for the original Greek, apparently λαγωός (Latin lepus, Lepus being the hare genus) means hare, but Χελώνη (chelon) just means turtle, no-doubt translated tortoise (-> (땅/육지) 거북) to clarify that it was walking with legs on land rather than swimming/sprawling with fins/webbed-feet.
Hares and rabbits are in the same family, but a hare isn't a rabbit. So in Korean they also have separate names.