All types of paprika are made from peppers belonging to the Capsicum annuum family. However, hot paprika is made using spicier peppers and will include the inner piths.
First off, capsaicin affects every animal species besides birds. These feathered friends don't experience the pain caused by capsaicin, which makes them the plants´ greatest ally in carrying seeds over long distances. This is a great example of evolution; it just makes sense to produce a compound that repels potential predators but does not affect your greatest seed carriers.