Both disciplines require the use of boots. The difference are great for the varried types of uses for both sports, but the main concern is for user comfort and control.
Bindings are as desperate as the varied boot choices, but the primary difference is that ski bindings let go of the ski where as you stay attached to the board aka deck for snow boards.
Both of these are similar yet physically dimensionally different, and again come in a huge variety of disciplines. The commanality resides in the materials and processes used in manufature of them. Alpine eludes to the camber and scarfed edges which help the rider control the board and or boards as they are flexed and twisted.