All the other directories under root
seem to be exactly what one would
guess them to be,
There is also /var, /mnt and /opt ;)
but these two seem
odd, I would have always guessed them
as user and temp.
Almost there. As Shawn said, "user" stands for "Universal System Resources" (though other resources according to the google indicates it stands for "Unix System Resources").
Is there some historical reason for the spellings?
Short cuts, abbreviations. Remember that commands in any operating system are meant for accessing both interactively and programmatically. In particular for systems administration where fast scripting is one primary concern, abbreviations, mnemonics are as good (or even better) than the full spelled word/command.
Also, back in the day, if you were connecting remotely through a slow-as-molasses modem, shaving a couple of vowels here and there would make your life easier (or less miserable if you were a sysadmin trying to find out what the hell is wrong with a remote box.)
As said before, it is not unique to /usr and /tmp (see /var, /mnt and /opt).
Also, it is not unique to Unix. Take DOS for example (chkdsk, for example.) Mnemonics where you shave off vowels are a powerful, handy concept.
Even in natural languages (like Semitic languages) the concept exists (where root of words are universally and almost unambiguously identified by 3-consonant groups.) It is an innate human mechanism for managing information.