To the original question…..
Yes, normally the standard Metric fixings are in the Coarse range. If you need M-Fine you'd have to seek them out especially.
However….
There are Metric Coarse range threads with alternative pitches so you may have been caught by this:
M3.5 X 0.6mm (Tapping drill 2.9mm)
M4 X 0.7mm (3.3mm)
M4 X 0.75 mm (3.25) Not a "preferred" thread, it seems.
M4.5 X 0.9mm (3.75)
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Those Tracy charts (quoted above) give all the standard M_ Coarse and Fine series by diameter, pitch and tapping-drill; and the tapping-drills recommended for all threads (BS, UN, BA, ISO), in readily-available mm diameters. The foot-note says these give around 65% full thread depth – the user to determine by experiment if a particular application needs an alternative depth.
Some of the less-common M-Coarse, and M-Fine, taps need tapping drills to 0.05mm – I assume reasonably easy to buy.
I have not used number drills for years and don't recall using my letter-drills set!
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Usually I avoid buying fasteners from the DIY supermarkets in favour of the building-trades chains, on the premise that they are supplying the trade so a bit more careful about quality – and often cheaper.
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I like those other mnemoics but stick to the "Trigonometrical Volcano" because a) SOHCAHTOA is the only acronym among them, and b) one of my other interests is Geology!
I would if I really have to, calculate tapping sizes but always endeavour avoid turning on the computer, navigating the wretched "cookie" traps, ferreting through the offered web-sites and so on, just to read a common, standard diameter established years afore The Home Computer.
When I use t'Net for more arcane information (rarely), I would probably print the tables for future reference.
Instead I have a reasonable library of reference-books for both the hobby and the trade; and two pairs of each of sets of look-up tables. They are the Zeus book, and the poster-size, double-sided Tracy Tools charts giving dimesion conversions and all the tapping sizes I'll need. One copy of each in the workshop plus a cheap, basic calculator (used in a protective freezer-bag); t'others plus scientific calculator near the computer for CAD reference.
Surprising invention, printed information, you know. I gather the principle goes back centuries, like that of Matrices but without their abstruse abstraction; but offering simple, rapid, direct reference not needing electricity and not going all unsupported on a Californian whim…. I wonder if it will catch on?