Like herring in the sea, these animals constitute a low and very important rung on the food chain for a lot of species, and their numbers fluctuate dramatically. When they do, the predator species fluctuate with them, but with a lag. Hence if there is a huge crash in a rabbit population which has been building up for several years, there are likely to be a whole lot of lynx or bobcats or foxes or coyotes left hanging out there on a biological limb that has been sawed off. Conversely, there are few of these predators around when the bunnies start to build up again, thus making the build up even faster than it would have been since there are so few predators around to check the growth. There are several sub-species of cottontails in the U.S., all fairly similar, and all very familiar to us with their little fluffy white powder puff tails.
Rabbits are less rangy than hares, and smaller and their young are born naked and helpless.
That should be enough about the natural history. Of course hares and rabbits figure large in myth and literature, and although the race was with a tortoise, not a turtle, if you wear the rabbit and the turtle, most people will pick up that you mean tortoise and hare.