"Screwed" vs. "nailed": why is the slang so different?

Nails

‘Nailing’ something is basically the equivalent of hitting the nail on the head. Hitting the nail on the head is, as anyone who’s ever tried hanging a picture on a wall knows, something that requires great precision and the proper application of force (and in my own case, often also the proper application of a few Band-Aids or similar).

As such, it is quite logical that ‘nailing’ something—i.e., fastening it with a nail by delivering one quick blow in exactly the right place to make it sit tight just where it’s supposed to—would acquire the meaning of “to perform or complete perfectly or impressively”.

Screws

Unlike nails, screws are not quickly fastened with one blow. Rather, they must work their way in slowly, and they do so while turning around constantly.

It is a very common metaphor, cross-linguistically, to indicate that something has gone wrong or is not as it should be by likening it to something that turns around or loops out of place. A screw is a good candidate for this. (Compare also the word awry, meaning ‘amiss, wrong’, which is etymologically from the now obsolete verb wry, which meant ‘to twist, turn, swerve’. That’s a similar development.)

If a nail gives the mental image of something going straight in, according to a linear projection, just the way it’s supposed to, a screw gives the mental image of something curving, looping, winding around, in an inefficient manner.

Further derivations

Once you’ve got those two basic meanings, it’s very easy to derive further slang terms from them. The nail-based ones are actually remarkably few in number, but the screw-based ones abound: you can screw something up (mess it up), you can be screwy (crazy), you can be screwed (ruined, done for), you can ‘screw it’ (forget it, leave it aside), you can screw someone over (cheat them), you can screw around (fool around), you can screw someone (as in, “Screw you!”, not-so-politely telling them to go to hell), etc.

Interestingly, both ‘nail’ and ‘screw’ can refer to sexual intercourse—but with the very fundamental difference (borne over from the basic meanings of the word) that screwing someone just refers, in a roundabout way, to the general ‘in-out’ motions performed during sex, while nailing someone indicates that there is a nailer and a nailee: one party is ‘using’ the nail, and the other party is implicitly likened to a wall that the nail goes into. In other words, it is quite common for a guy to brag to his friends that he ‘nailed’ a girl; but not very common for a girl to say that she ‘nailed’ a guy.

On, the other hand "I nailed her last night" and "I screwed her last night" would be taken as having the same meaning.

I'd also note that screwed has yet another meaning, if you "screw up a bit of paper" then you are crumpling it in a ball as you might do on discovering you've messed it up. It's quite possible that "I screwed it up" comes from this usage of "screw" rather than the fastening. "Nailed it", as noted by Janus, may come from "hit the nail on the head".

Seen in this context it doesn't seem that unreasonable that apparently similar concepts have come to have very different slang meanings.

“Screwing” and “nailing” are slang for the same act: “f*cking,” i.e. penetrating during intercourse. Notice there are different connotations to “f*cking.” On one hand, “f*cking something/someone up” could mean to ruin, damage, destroy it/them; e.g. the group project, or someone’s face. On the other hand, “f*cking something/someone over” could have the implication of holding dominance over it/them.

So when someone says “I screwed it up”, they’re using the metaphor that they “f*cked it up” so that it’s ruined. They might also mean that they twisted it (because screws twist) to a point that it’s no longer functional. And “nailed it” means they defeated it, dominated it, held power over it.

A wild guess might be that the circular motion required to operate a screw, might render the expression "screwed" a sort of euphemism for more vulgar expression like "fucked up", and so on.

A nail, on the other hand, can keep stuff tighly on a wall or piece of wood and once completely nailed down, may be even hard to easily extract... :-)

(Just guessing)