There are three other types of transformations in a plane. They are all transformations that move a pattern in a way that the pattern still matches the original pattern exactly. Let's look for the other three types. We could slide the whole pattern sideways. This kind of symmetry is called a translation.
All translations have a direction and a distance.
Part of the definition of a tessellation is that it is a repeating pattern. I could spin the pattern around a point, or rotate the pattern. That transformation would leave the pattern unchanged. This transformation is called rotation. Rotations always have a center, and an angle of rotation.