There have been previous exhaustingly long threads on nomenclature with the usual fall-outs over definitions, so I won't go into all that again, but happily agree with Sharon's summary!
I play a B/C but rarely play in either of those keys, especially not in B! (A misconception from a few that those are the only keys you can play in). I do use the left hand a bit, mainly in slower tunes in G or D, as I have both on the pull and the push. And I can play in ANY key in the right hand, provided I can find the notes, so in that sense less restrictive than the D/G.
But the speed thing: yes, it's the bellows along with tune which really determines how fast you can play. In The key of A, I can get long runs of notes all on the pull, but try tunes like e.g. Soldier's Joy (D), Flowers of Edinburgh (G) and you're talking a helluva lot of alternate pull and push, and tho my fingers may work fast enough, the bellows won't. And let's keep hornpipes as hornpipes, not turn them into reels, please!