A linnet is a bird. Its Latin name is Acanthis cannabina. It is one of the smaller finches. It is gregarious and a cheerful little chappie, known for his singing. The Victorians kept linnets in cages. We don't do that anymore.
In Aesop's fable, the English translation is the tortoise and the hare. The tortoise improbably won (perhaps something about the hare lacking the spirit of Janteloven?) but the winner was not a sea creature, a turtle.