Having never used one, please excuse my ignorance.... but why are the lathe attachments of a lesser capacity than the standalone? I understand if the lathe has a smaller capacity but they seem to sell an attachment for a 14inch delta on their site...
I understand what you call your ignorance and it is ignorance at all . You are not the first to ask about that and won't be the last and hope I can clear up your curiosity about it.
Having never owned a lathe mounted one I cannot say from experience.
I am only going by what the ringmaster company says and videos I have viewed as well what some of the members in the dedicated Ringmaster Lathe Turning board in my own site say about it.
Some have said they can turn up to 10" and some only 8" because on their particular model of lathe mounted ones .There are many lathe mounted models to fit various makes and models of lathes. One size does not fit all when it comes to lathe mounted ones. I believe it has something to do with the thickness of the mounting plate and hardware above and below the lathe bed that is required in order to mount it whereas the stand alone model is fastened to a 3/4" plywood base with no obstruction .
It has absolutely no bearing on the size of lathe being a 12" or 14" or 16" or 18" . .
With that said I sure wouldn't want a lathe mounted one . I know a few that have got discouraged and gave up soon because of having to mount it and line it up before ever using it and then their lathe can't be used for other types of turning unless they take it all off again . Even though a bowl can be sanded right on the RM , I use my regular lathe for sanding all my bowls and for some other jigs I have made for putting a solid no hole base on the under side of segmented bowl bottoms. It would drive me nuts forever taking a lathe mounted one off to use the lathe for other things and have to put it back on to cut more rings . .
I much prefer the stand alone model. There are only two models of those and are exactly the same in every respect apart from one having a VS function and both will cut full 12" rings.
Also , with a lathe mounted one , , if you decide to upgrade to a different lathe some time in the future you will have to buy a different model RM to fit the new lathe if it is a different make and model to your previous one.
You might notice messages here and there about ones that have cut a few rings and even shown pictures of non completed projects when they bought a lathe mounted one years ago but have nothing to show since . It sits somewhere in a corner collecting dust . I probably would have got that discouraged as well if I had not bought a stand alone model .