What is the difference (in terms of usage and connotation) between "loath" and "loathe"?

'Loathe' is a verb used to indicate repugnance:

I loathe Brussels sprouts.

'Loath' is an adjective suggesting unwillingness or reluctance:

I am loath to eat my Brussels sprouts.

As for pronunciation, they both rhyme with 'loan' as far as the vowel sound is concerned, but 'loathe' ends with a 'th' sound as in 'the', whereas 'loath' has a 'th' as in 'thing'. This is based on my experience as an Australian English speaker who rarely says either of these words!

There are several pairs of words in English where the verb has a voiced 'th' (/ð/) and the other form has it unvoiced (/θ/).

Usually there is a difference in spelling ("loath"/"loathe"; "wreath"/"wreathe"), but sometimes not ("mouth"/"mouth"). Sometimes the vowel sound changes as well ("breath"/"breathe"; "bath"/"bathe").

In most cases the 'non-verb' is a noun, but in this case "loath" is an adjective. However it is a slightly odd one, in that you can say "I'm nothing loath to ... ": I can't think of any other words that will go in this construction.

"Loath" is also rather rare in modern English.