E-Bay sellers typically list the steady rest by the part number that is cast into the main piece. Few people know the original model number or order number of the completed assembly, unless they have old catalogs.
The open type for Atlas and Atlas-made Craftsman 12" lathes has part number L3-326 cast into the lower part of the body. This open type can support work up to about 3-3/4 inches diameter maximum using the standard fingers.
The closed hinged-type for the 12" lathes will have part number 050-028 cast into the lower body, and part number 384-003 cast into the upper hinged part. This type will support work up to about 2-3/4 inches diameter. (the upper hinged part will be the same for the 10" version so watch for the number that is cast into the body of the lower section.)
I have both. I prefer to use the hinged type as it is stiffer and is easier to move on the ways with work mounted and it is easier to insert or remove stock from the lathe without mucking with the fingers, but for anything over about 2-1/2" I use the open type.
The models for the 10" lathe can be used on the 12", you will need to fashion a 1" riser block to accomodate for the difference in swing and the performance will be the same, but it would be impractical to use the 12" model on a 10" lathe. - I'm not saying it can't be done, it would be rather awkward and not recommended.