In reply to Glyn Davies:
> But where I have gone for an onsight, taken a single fall, had a shake-out, gone straight back onto the rock and made the move and finished the climb, I assume it's dogged, even if it was just one failed move ?
Yes.
> If I'd lowered straight down from the fail and re-climbed immediately it would definitely be a 'ground up'.
Only if you pulled the rope (and removed the gear, if you wanted to be really pedantic/purist). If not, it would be a "yo-yo."
> I'm just confused about whether me finishing the route completely before reclimbing the route makes it a ground-up or a redpoint/headpoint?
As I understand it, it's not "ground up" because when you did the clean lead, you were familiar with all of the route; you weren't venturing into the unknown on the part of the route that came after your first fall.
Even though you didn't put a top-rope on the route, you still "practiced" it (in a very minimal way) by pulling back on and climbing the rest of the route after falling, thus familiarizing yourself with it (a.k.a. "hangdogging"), instead of immediately lowering off.
It doesn't mean your clean lead is "impure"; it's just not a ground-up ascent because that's not what the terminology means.