"AWT WW" and "Magnus" collets are both stamped only Whitcomb on the side. The Derbyshire collets are stamped Derbyshire plus the lathe/collet size. There are three Derbyshire collet types.
1. Derbyshire WW - the mostpoplar type and the same as the original "AWT WW". These collets are stamped Derbyshire Small, Derbyshire WW or Derbyshire Webster Whitcomb. The collet body is 8 mm and the thread is .275 inch by 40 t.p.i. with an ordinary Vee profile.
2. Derbyshire Magnus-Elect - these are the same as the AWT 10 mm collet and were called the type "D" by Levin. The body is 10 mm and the thread is 10 mm by 1.0 mm with a buttress profile.
3. Derbyshire Large collet. I believe this style was invented by Derbyshire. The body is the same as a WW collet (8 mm), but the thread is 8 mm by .70 mm or 36 t.p.i. with a buttress profile. I have never seen the actual thread pitch described in a Derbyshire catalog and even under a microscope I cannot tell the difference between .70 mm and 36 t.p.i. I have a few collets made to Derbyshire large dimensions by Hardinge. They are stamped Hardinge 1DN. But I have never seen any other copies of the Large collet.
The advantage of the Large collet is that it has a larger diameter through bore, allowed by the larger thread. WW collets can have a maximum through hole of 5.0 mm (3/16 inch). The Large collets have a maximum through hole of 6.35 mm (1/4 inch). So a WW lathe is limited to holding up to 5.0 mm diameter long parts or bar stock. The Large lathes can go up to 6.35 mm (1/4 inch) diameter long parts or bar stock. The Magnus and Elect 10 mm lathes can hold up to 8 mm (5/16 inch) diameter long parts or bar stock.
AWT WW lathes and other brand copies of the WW pattern lathes use only the WW collets, because the spindle bore is too small for the larger drawbar required by the Large collets. Derbyshire's first lathes in 1911 could use either Small (WW) or Large collets. In 1911, he called his WW collets Small because he did not yet own the Webster-Whitcomb trade name. I have a Derbyshire collet box with a label copyrighted 1911 that illustrates his WW style lathe and the Large and Small collets. I think Derbyshire stopped using the Small name after he got the right to use the WW name in 1918.
The Derbyshire Large collets are very scarce, so it may be assumed they were never popular - though they were still listed in the 1982 catalog. Derbyshire catalogs from 1952 and 1965 listed the WW and Large lathes as separate items though as far as I can tell, the only difference in the two models was the collet and drawbar. The Large collet has no size advantage over the WW except in the bore range of 5.1 to 6.35 mm, and then only if you want to hold a long part. Judging by the scarcity of number 51 to 64 WW collets, these sizes were of use to very few watch lathe owners. WW collets are made in sizes all the way up to 8.0 mm or 5/16 inch, but they only have a relatively shallow stepped bore in the sizes over 5.0 mm. The Large collets do have a strength advantage inherent in the larger diameter, buttress profile thread. The drawbar threads would be stronger and wear longer in an industrial environment such as a watch factory.
So, the bottom line is that Derbyshire 8 mm lathes may all be used with the common WW collets if you have a drawbar with the standard .275-40 threads. That size tap is usually available on eBay, if you need to make a drawbar. A drawbar made to correctly fit a Derbyshire WW or Large lathe will have a larger outer diameter than one made for another brand of WW lathe, but a skinny drawbar will still work if it is the correct length.