“Slang” is a remarkably difficult thing to pin down. The Oxford English Dictionary defines it (noun entry 3, sub-entry 1.a.) as “The special vocabulary used by any set of persons of a low or disreputable character; language of a low and vulgar type” (harrumph!) followed by a more modern definition (n.3, 1.c.) “Language of a highly colloquial type, considered as below the level of standard educated speech, and consisting either of new words or of current words employed in some special sense.”
So, I would say that “Alice and Bob screwed every night on their honeymoon” is slang (and perhaps mildly vulgar); “screwed” is a “current word” that is here being “employed in some special sense”. (Alice and Bob are having sexual intercourse, not assembling pre-fab furniture.) “Alice and Bob fucked every night on their honeymoon” is vulgar, but not slang, since “fuck” is an old English word (of Anglo-Saxon origin) literally meaning “to have sexual intercourse with”. “Alice and Bob had sexual intercourse every night on their honeymoon” is neither slang nor vulgar (although vulgarity is also a bit hard to pin down, and really prudish types will likely consider that statement to be a bit indelicate; but perhaps the statement is part of some medical report, after Alice and/or Bob suffered some kind of sexual-intercourse-related injury). “Alice and Bob made love every night on their honeymoon” is more “polite”; it’s also euphemistic, but such euphemisms probably wouldn’t be considered “slang”.
“Bob screwed the new bookshelves together” is not slang, as the word “screwed” is here being used literally, and not in any special (colloquial or non-literal) sense; nor is it vulgar (although some low-minded or immature types might snicker at any use of the word). “Bob got totally fucked by Alice in the divorce settlement” is both vulgar and slang, since clearly we are no longer talking about literal acts of sexual intercourse.
Just to round it out, “each bathroom tile has a groovy side on the bottom and a smooth side on the top” is not slang; “Whoa, Bob! Those new bookshelves are totally groovy!” is not vulgar, but is presumably slang (unless for some reason the new bookshelves have grooves on them).