Robin,
Machinists, expecially new hobbiest ones, have a tendency to be sloppy about nomenclature. In fact, hobbiests in general are bad about this. Generically, there are two types of threaded devices that work by sticking them through the hollow spindle from the left end. They are called draw bars and draw tubes. Draw bars are (almost always) solid, and have male threads. Draw tubes are hollow and have female threads.
The most common draw bar in the English speaking world is 3/8" in diameter and has 3/8"-16 threads. There is no "standard" draw tube. They are identified by the collet type that they fit, most of which are of different outside diameters with different pitch threads.
What you probably have is the Atlas cutter holder set for 3MT (or MT3). It consists of a 3.8"-16 draw bar. a 3MT to 1/2" diameter cutter holder with set screw, and four reducing bushings. And I will throw in here that you never ever want to use a Weldon style (with the set screw flat ground on the side of the shank) cutter other than one with a 1/2" dia. shank that does not require a bushing. Those are safe to use. But if you put a smaller shank diameter one into the appropriate reducing bushing and tighten the set screw onto the flat in the bushing with the flat on the cutter right under the set screw, you will probably never manage to remove the cutter and bushing from the 3MT cutter holder.
Anyway, this setup is used only for holding milling cutters whose shanks fit the holder or one of the bushings. It could be use to hold a short work piece of the proper diameter, but the set screw will mar the surface. So you do not want to try to use it for that.
The draw bar is made for tightening tools that have a taper that matches the taper in the lathe or milling machine spindle. The only collets that it will tighten (close) on your machine are 3MT collets, which only come in 1/16" diameter increments. You can use 3MT collets for holding short work pieces but the work piece diameter must be withing about +/- 0.007" of the collet diameter.
If you want to do mill work with the Atlas milling attachment mounted in place of the compound, it sounds as though you have what you need so long as your cutter shank diameters are 1/4", 5/16", 3/8", 7/16" or 1/2". But if you want to use collets for holding work to turn, face or thread on the lathe, aside from short work pieces in the range 1/16" to 3/4" by 16ths that 3MT collects come in, you need something else.
The three collet types that are commonly used on an Atlas 10" or 12" are 3AT (which is what Atlas/Clausing used to sell), 3C, and any of the European type ER collets. The first two require a matching draw tube and a 3MT to 3AT or 3MT to 3C closer adapter. The ER collets require what's usually called a collet chuck, of which there are two types, those that screw onto the spindle threads (and allow the work piece to extend back through the spindle) and those built onto a 3MT arbor secured by a draw bar (that don't).
The pro's and con's of these three types of collets is another subject (which I think this thread was originally about).