Actually this question can be answered from various perspectives. According to physics, both of stiffness and rigidity are a lot different from each other.
From daily usage point of view,
Rigid
1. An iron rod is Rigid
Stiff
1. My muscles have become stiff after an unusually long exercise.
2. The door hinge has become stiff. May be we should think of applying some grease.
I think you can make out the difference from the above examples. Rigid is something, that is not bendable under normal circumstances. And stiff is usually used for temporary states.
Also, you can use "rigid" for describing the mentality of a person. For instance, "He has got a rigid mentality.