Usually in shop-floor terminology, the terms collet and chuck are used in contradistinction; users speak of holding a workpiece or tool with either a collet or a chuck. This usage refers to the same distinction as does speaking of using either a collet chuck or another type of chuck (scroll chuck, independent-jaw chuck, etc.); the two usages are different ways of saying the same thing. The difference lies in how one thinks of the overall chain of connection between the machine spindle and the thing being attached to it (workpiece or tool). In general terms, the overall system of holding constitutes a chuck, but practically, the receiving sleeve for a collet is often integral with the machine spindle, and from the point of view of naming the parts that are added on to the spindle, they are either a collet (± cap) or a chuck (such as a scroll chuck).
The collet's advantage over other chucks is that it manages to combine all of the following traits into one chuck, and this combination is highly valuable in an environment of repetitive part production:
Of the above traits, scroll chucks offer always № 1 and № 2; usually № 3; to varying extents № 4 (depending on the situation); but not reliably № 5 (if you get it, you simply got lucky). Independent-jaw chucks offer always № 3; usually № 4; reliably № 5 (but at the expense of paying a skilled user to spend time achieving it); never № 2; and generally not № 1. Meanwhile, a collet chuck can deliver all 5 reliably, and with no need for a skilled user. (№s 3 to 5 do depend on the object being clamped closely matching the size and shape of the collet's clamping surface. This constraint is usually not a problem when the object is good-quality bar stock; the shank of a non-abused drill bit, reamer, endmill, etc.; or a previously machined part that is being rechucked for additional cutting operations.)
On a wood router (a hand-held or table-mounted power tool used in woodworking), the collet is what holds the bit in place. In the U.S. it is generally for 1/4 or 1/2 inch bits, while in Europe bits are most commonly 6 mm or 8 mm. The collet is hexagonal on the outside so it can be tightened or loosened with a standard wrench, and has threads on the inside so it can be screwed on to the motor arbor.
There are literally hundreds of designs of collet used in the metalworking industry. There are some common standardized designs, like the 5C or the R8, and then there are many proprietary designs that only fit one specific manufacturer's equipment. Collets can range in holding capacity from zero to several inches in diameter. The most common type of collet is one that grips a round bar or tool, but there are collets for square, hexagonal, and other shapes. In addition to the outside-holding collets that are so common, there are collets that are used for holding a part on its inside surface so that it can be machined on its outside surface (basically, akin to an expanding mandrel). Furthermore, it is not uncommon for users to make a custom (bespoke) collet to hold any unusual size or shape of part. These are often called emergency collets (e-collets) or soft collets (from the fact that they are bought in a soft (non-hardened) machinable state and cut as needed to fit). Yet another type of collet is a step collet, which steps up to a larger diameter from the spindle (analogous to how a mushroom cap is larger than the stem). Step collets allow the holding of rather large workpieces, as long as they need not pass into the spindle through-hole—for example, disc-shaped workpieces.
In the accompanying photo, the two top left collets are the side and end view of one style of collet; the two right collets are from a smaller range. The lower image is of a disassembled pin chuck that is used to hold small drills or workpieces. The leftmost part is the body, the collet is shown protruding from the body, and the nose cap is separate, on the right.
In use, the part to be held is inserted into the collet, and then the collet is pushed (via a nose cap) or pulled (via a drawbar) fully into the body (which has a taper to match the collet machined into the front). When the nose cap or drawbar is tightened properly, enough force is applied to the collet that the tapers at the front and back of the collet are pushed into their matching tapers, causing the collet to constrict in diameter. This constriction exerts considerable force onto the shank of the workpiece or tool that is being held in the collet. It is then securely held against any forces it may encounter during normal operation.
In semiconductor industry, a die collet is used for picking a die up from a wafer after die cutting process has finished, and bonding it into a package. Some of them are made with rubber, and use vacuum for picking.