Cakes go hard when they are stale. Biscuits go soft when they are stale.
So, what about a ship's biscuit?
From an American point of view, none of the terms biscuit, cake, or cookie is an appropriate descriptor for ships biscuit, which is also known as hardtack and by other terms. The image below is from wikipedia's article about hardtack.
The article says
From that description and from the picture, cracker evidently is the most appropriate term.
Note, the previously-linked biscuit article begins by distinguishing American usage (where biscuits are like small breadrolls except often leavened with soda, not yeast) from British usage (where biscuits are like cookies or possibly like crackers).
British biscuit is what Americans call cookie; US biscuit is close to what British speakers call scone. Ship's biscuit is about the only modern use of biscuit which preserves its original sense of "twice cooked" (Latin biscoctus French bis cuit—but the French spelling is a late-18th-century affectation; the word had been thoroughly naturalized as bisket, bisquet, bisky &c by the 14th century).
The extreme hardness celebrated in the name jwpat7 offers was a by-effect of a process designed to render the bread as dry as possible, to retard spoilage and reduce weight.
See OED 1.
What makes an item of food is a biscuit or a cake is something that the UK government contested in court as part of the Jaffa Cake trial. The Tribunal came to the following conclusion:
Consequently we can conclude that whether an item is a cake or a biscuit is much more complex than merely whether the name contains the word "biscuit" or that "cakes go hard when they are stale. Biscuits go soft when they are stale."