OK,all understood.
"1st taper" taps are used to start ALL threads (and from the name you'll guess they have the biggest taper, starting with a much small dia at the bottom and gradually tapering to max at the top). This makes it easier to start the tapping, especially if tapping by hand.
"2nd taper" taps are not used so frequently, and have rather less taper - i.e. more full-ish dia - than 1st taper taps do. And "plug" taps have very little or almost no taper. You normally only use the plug taps when you want to tap into a blind hole (i.e. a hole than doesn't go all the way through the work piece, but you still want to screw into the full depth of the hole)
From that you'll probably guess (correctly) that a lot depends on the thickness of the work piece as to which of the 1st and/or 2nd taper taps you'll need. If tapping into thin-ish sheet or thin plate, and if the hole goes all the way through, then you can probably get away with just 1st taper, though when the job is thicker, and/or you need a better thread with more full screw thread engagement, and/or if it's harder material (harder than MS), then 1st followed by 2nd is the "proper" way. And plug is, as above, normally only used for tapping blind holes.
For all metric screw threads there are 3 separate ISO "norms" (standards). "Coarse", "Fine", and "Extra Fine". By far and away the most common you'll come across every day is the Coarse - they're so common that often the screw/bolt, and even the tap is NOT marked Coarse (but on the taps, the "pitch" (see below) IS usually marked.
The Fine threads are much finer (!!) - in both cases this means the length you move along the thread with 1 revolution. For example, 8mm Coarse (the everyday jobbies) have a pitch (commonly, but incorrectly often called "TPI") of 1.25 mm, whereas the 8mm Fine have a pitch of 1.00. What this means in everyday language is that on the 8mm coarse, 1 rotation of a "nut" on that bolt/screw will move the "nut" along the bolt/screw by 1.25mm. On the 8mm fine, 1 rotation will give you a lengthways movement of only 1.00 mm.
As said, the coarse is the everyday thread, but on electrical and electronics goods, computers, etc, fine and extra fine are more common (because the parent metal that the bolt/screw screws into is very often pretty thin sheet metal formed into a chassis or something). Extra fine has a pitch of 0.75mm.
Sorry it's long but hope it's clear and that it helps you (as my good lady always says "Nobody fell down from the stork knowing it all!").
