The rail is the part of the railing system that you touch with your hand as you go up and down a stair.
The post (also called a newel) is the vertical structure that connects the stair or floor to the railing system.
Spindles, which are vertical wood or metal structures, are interspersed between posts to provide a safety barrier along the stair system.
Shoe is the bottom plate that spindles (or glass) are set into.