Hares and rabbits are very different from each other.
The hare only belongs to the genusLepus, but their are many genera the rabbit belongs to - Pentalagus, Bunolagus, Nesolagus, Romerolagus, Brachylagus, Sylvilagus, Oryctolagus, Poelagus.
Hares are larger and faster, generally longer ears and have black markings on their fur. Leverets (baby hares) are precocial, which means, unlike rabbits, are able to see almost immediately after they're born. Baby rabbits are called kits, kittens or bunnies. Hares are also have stronger limb muscles. Hares have not been domesticated, so you can't have one as a private pet (yet), or at least legally.
Hares do not neccesarily live in warrens and burrows for protection; they rely on speed for that.
Hares are more solitary and rabbits are extremely social.