Not necessarily two kinds of pain, but there is pain and there is suffering.
Buddhists call it the two arrows. The first arrow is pain. The second is suffering.
When one is struck by the first arrow, one experiences pain. That is inevitable. Whether it be physical pain or emotional pain, the pain will be there, and one hopefully learns from the experience and becomes "stronger."
The suffering is optional. One can move out of the way of the second arrow and avoid being struck again. The second arrow, in essence, represents how one reacts to being struck by the first arrow. Sorrow, worry, anger, blaming oneself (or another) is the suffering represented by the second arrow.
One will inevitably experience pain, but the suffering is optional, or as noted in the "House of Cards" quote, unnecessary.