Two holes, two different sizes, and confusing them wastes parts. A tapped hole is drilled smaller than the screw so there is metal for the thread to be cut into. A clearance hole is drilled larger so the screw passes through freely.
The metric rule
For metric threads, the tap drill is the major diameter minus the pitch. M6 has a 1.0 mm pitch, so the drill is 5.0 mm. M4 at 0.7 pitch gives 3.3. M3 at 0.5 gives 2.5.
Check those against any published tap drill chart and they match, which is the useful thing about this rule — it is not an approximation of the chart, it is where the chart comes from.
The exception is M8 at 1.25 pitch, where the rule gives 6.75 and charts list 6.8. That is simply because 6.8 is a drill that exists and 6.75 is not, in most sets.
The inch rule
For unified threads, the tap drill is the major diameter minus one divided by the threads per inch. A 1/4-20 gives 0.250 minus 0.050, which is 0.200 — and the standard tap drill for 1/4-20 is a number 7 drill at 0.201.
3/8-16 gives 0.3125, which is exactly a 5/16 drill, and that is what the chart says.
Number-size screws work the same way using their actual major diameters, which are not obvious from the number: a #10 is 0.190 inches, not a tenth of anything.
Thread engagement, and why 75 percent is a thing
A larger drill leaves less material, so the tap cuts a shallower thread — less engagement. Engagement of 100 percent is not actually achievable and the standard figures land around 75 to 80 percent of theoretical.
Going deliberately lighter makes tapping much easier and reduces the chance of snapping a small tap, at a modest cost in strength. In a blind hole in tough material, that trade is often worth it.
For most work the standard figure is right. The lighter option exists for hand-tapping small threads in stainless, where a broken tap is a much worse outcome than a slightly weaker thread.
Clearance holes
Clearance sizes come from a standard — ISO 273 for metric — in three series: close, normal and medium, and loose or coarse. Normal is the default and is roughly the screw diameter plus ten percent.
M3 normal is 3.4 mm, M4 is 4.5, M5 is 5.5, M6 is 6.6, M8 is 9.0. Those are worth knowing by heart if you make things.
Close fit is for alignment-critical joints where you want the screw to locate the part. Loose fit is for where two holes have to line up despite tolerance stack-up, which in practice is most brackets.
Threading into printed plastic
You can tap a thread directly into a printed part and it will hold for light duty. It will also strip the first time someone overtightens it, because there is no elastic reserve in a plastic thread.
Heat-set inserts are the right answer for anything that will be assembled more than a few times. They need a hole sized for the insert rather than for the screw — the insert manufacturer gives that figure.
A captive nut in a pocket is stronger still and costs nothing but design effort. Design the pocket a few tenths oversize and add a chamfer, because printed pockets always come out tight.