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

[glynster]

Is there a metric equivalent of TPI (Turns per inch) in relation to leadscrews?

Apologies if this has been done to death, I dont even know what proper terminology to search for. I am building a solsylva machine - mostly to learn some basics of CNC machine building - and the plans are in imperial measures. I have converted all bolts and screw sizes to metric to make sourcing components easier and cheaper. However the plans call for a "36inch x 3/8-8-4 Start 2 Turn Leadscrew"

I simply cannot find such a thing anywhere. I figured I could use a 10mm leadscrew instead of a 3/8" as they are near enough equivalent. But what is the metric equivalent of 2 TPI. Would that simply be 12mm or 13mm per turn? If so what terminology is used to describe such a thing and what do the "8-4" stand for in my above example in bold?
I find the terminology of leadscrews extremely confusing. Any help would be appreciated.

Thanks