Tetragonal lattices result from stretching a Cubic lattice along one of its lattice vectors, so that the cubic becomes a rectangular prism with a square base(a by a) and height (c, which is different from a).
There are two Tetragonal Bravais lattices: the Simple-Tetragonal(from stretching the Simple-Cubic lattice) and the Centered-Tetragonal(from stretching either the Face-Centered or the Body-Centered Cubic lattice).