Morse Taper shanks are tapered from one end to another. They fit into tool holders with the same taper. They allow efficient transmission of torque to the drill bit and provide accurate, centered placement in the tool holder. A tang at the end of the taper is used to eject the drill bit by pushing a drift-pin into the slot, which pushes the shank down and out.
Round shanks are the most common drill bit shank. They are usually the same size as the drill bit cutting diameter. This style fits into the widest range of tool holders.