I do see they have up to 15ss but not the 20SLa
To be honest, in my view it would already have been difficult to tell a difference between an ATS20, ATN20 or ATN20SS and an ATS15, ATN15 or ATN15SS back in the day - and by now it'll most likely make more of a difference, how well or not so well the individual exemplars have aged.
Mind you, however, that BBE's compatibility info isn't quite correct in this case. I.e., while BBE claims the ATN13 and ATN14 to be compatible with the AT15/20 family bodies, that actually isn't true, because the connector block of the AT15/20 family bodies is a bit wider than the generator shell, which doesn't apply the bodies of the AT13Ea and AT14Sa (and the other models with the same body and matching needle shape, like for example the AT12d, AT13d, "the other AT12E and AT13E" (the ones with the original needles ATN12E and ATN13E rather than the ATS12 and ATS13), the AT13EaV/EaX et cetera). So the original needles for these models won't really properly fit onto AT15/20 family bodies. And the other way around it actually isn't true either, 'cause original AT15/20 family needles have too high side walls to properly fit onto AT13Ea, AT14Sa (et cetera) bodies. That's why there used to be some special 3rd party replacement needles with a combo shape with side walls, that were both lower and also less thick at the rear end, so that these replacent needles would actually fit onto both body shapes - but due to being way less good than the originals, I wouldn't recommend these replacement needles and rather just mention these, as the existence of these may be resposible for the false compatibility info regarding the original needles.
Greetings from Munich!
Manfred / lini
P.S.: For illustration, see for example over there on HifiWiki:
https://www.hifi-wiki.de/images/0/04/AT20SLa_05.jpg Here you can easily the wider connector block on the AT15/20 family body and the matching non-uniform inner width of the needle. Whereas on this rotating GIF by Turntableneedles you can easily see the uniform inner width of an original ATN13:
https://www.turntableneedles.com/assets/images/ProductImages/202-DEM.gif And to see the difference in side wall height you could compare the side view of that ATN13 with the side view of this rotating GIF of an ATN15SS:
https://www.turntableneedles.com/assets/images/ProductImages/203.gif
And while I'm at it, I might as well finally also include the quite closely related Signet TK1E to TK7SU family. See for example the body of a TK5E over there:
https://img.canuckaudiomart.com/upl...4aa1b-audiotechnica-signet-tk7e-cartridge.jpg And for a rotating GIF of a TKN3 see there:
https://www.turntableneedles.com/assets/images/ProductImages/jan07/signet-3.gif As one can see, in case of these Signet bodies the connector block itself has a tiny width step, so that the connector block gets a tiny bit wider towards the rear end - and that tiny bit is just enough, so that an ATN13 or ATN14 (et cetera) won't properly fit onto a TK1E to TK7SU family body, whereas an AT15/20 family needle will fit.