Shadow mapping deformation

I was noticing that the shadow is deformed. It appears that the order that the vertices are sent is important. After paying very careful attention to vertex order and switching from a GL_QUAD to a GL_TRIANGLE_STRIP, the deformation has mostly disappeared.

Something that is confusing me is when I send over a rectangular plane and not a square plane, the shadow seems deformed.

I'm not sure why this is happening. Here are the screen shots:

Square plane, shadow looks correct to me:

Rectangular plane, deformed shadow: