As you notice there are lots of different types of collets and some have been obsolete for a long time.
Most lathes use the "MT" or Morris Taper series as do many drillpresses. The MT can have an internal thread, a tang, or nothing else to retain them other than friction. They have been used on some small milling machines too but are mainly for drills and lathes that see little to no side forces that would dislodge those collets/work.
Many of today's milling machines use the popular Bridgeport R-8 collet series. They too use an internal thread for a drawbar retention. The R-8's look like a small trumpet. They are intended mainly to hold tooling rather than work. They will hold up to about 3/4 inch diameter round bits etc.
The popular work-holding collets are the C-series such as the C-5's. They are trumpet shape too but fatter than the R-8's and they have external threads that are retained by a tubular drawbar. That system allows work (usually rods, gun barrels ...) to reach through the collet and out the back.
As far as I know the modest spindex type indexers are not worm-drive but simple direct turned devices that are stopped by a peg and lock-clamp at a desired radial position. They usually use the C-5 collets for small (1 1/8 inch diameter max) rod stock. You could likely make a small faceplate to go on a spindex type indexer maybe even a small 4-jaw chuck to hold odd shape work. However I don't think you can rotate that work and mill at the same time as can be done with a dividing head (those really expensive things).
Hope this sheds some light on this collet stuff.