A collet is a segmented sleeve, band or collar. One of the two radial surfaces of a collet is usually tapered and the other is cylindrical. The term collet commonly refers to a type of chuck that uses collets to hold either a workpiece or a tool but has other mechanical applications.
Several machine collets (top and centre) and a dismantled pin chuck (below).
R8 Collets
From left to right 5C, 2J and 3J collets. All 1" workholding size.
A chuck is a specialized type of clamp used to hold an object with radial symmetry, especially a cylinder. In a drill, a mill and a transmission, a chuck holds the rotating tool; in a lathe, it holds the rotating workpiece.
A chuck on a power drill, showing the teeth that engage with the key
Self-centering three-jaw chuck and key with one jaw removed and inverted showing the teeth that engage in the scroll plate. The scroll plate is rotated within the chuck body by the key, the scroll engages the teeth on the underside of the jaws which moves the three jaws in unison, to tighten or release the workpiece.
Top: an assembled keyless chuck. This type of chuck is tightened by twisting the body using firm hand pressure only. While convenient, this feature can cause the chuck to tighten too much when high torque is applied. Bottom: the widely used keyed type of drill chuck with its key. The arbor is shown separately to the right. These chucks require a toothed key to provide the necessary torque to tighten and loosen the jaws. When the key is turned its teeth mate with teeth on the chuck, turning an internal screw which in turn moves the threaded jaws in or out along a tapered surface. The taper allows the jaws to clamp
Two pin chucks. The top one is assembled, the lower one shows the body and nose cap assembled with the collet piece below it.