Flat Metal: Mostly made of brass and mostly with grooves into which the shank and hook retract. Note the one on the left with a cross-shaped slot into which the hook retracts, and the one on the right which is made of japanned tin with two different sized sliding hooks.
Wire Loop: Between which the shank and hook retract. Note the center double hook which does not allow both hooks to retract simultaneously, but instead allows the crocheter to choose between extending one of two different sized of hooks.
Cylindrical: Leftmost is a bone cylinder with brass neck and tightly fitted shank with a knob for extending and retracting.
Second is a tin cylinder with a hook which is extended and retracted by a tightly cinched shank and knob.
Third is a nickel cylinder with tightly fitted shank with a bump on it for extending and retracting.
The leftmost hook is attached to a spring inside a tin cylinder. The hook is extended by pushing a knob forward and locking it in a notch.