It's the nature of diminished chords, using the usual formula of 1-3-5-7. Start with a root, make the next note up a minor third. The 5th is then diminished, and the 7th also.So, using your case, root=F, min3=Ab, dim5=Cb and dim7=Ebb. Not really 'stacked minor 3rds', but effectively the same.
So, yes, you're correct. That's the same sounding chord as B dim - B, D, F and Ab. Slightly different names, technically, due to different roots, but effectively the same sounding.
As there are only 12 notes available in Western music, that means there are, in a way, three 'different' diminished 7ths, because, as you saw, by the time you move up chromatically through those three, the next will contain the same notes as the first, and so on. They usually get named from the lowest, or root note, but I've seen the same chord shown with two different names in the same piece, probably due to each needing, or being given, a different root note.