TPI in metric? And a few other leadscrew confusions for newbie

[Neale]

No, it will be labeled as 12mm, 3-start or 6mm, 2-start or whatever. Not 4mm or 3mm.

Problem is that you should really talk about "lead", which is the amount a nut would move for one turn of the screw, and "pitch", which is the distance between adjacent crests on the thread. But most of the time we tend to say pitch instead of lead, hence the ambiguity.