There are a lot of these. It's useful to know that, if you hover over a selection in your IME, a thing will pop up briefly describing the differences between all possible kanji selections of an individual word.
Psy wrote:Simple but seldom taught, it would seem:
直 = repair of something broken. (fix) 治 = return to health from illness. (cure)
If you think that's fun, try かえる.
You could say that when someone is sick and on-the-mend as "naosu". For example if someone notices you're sick you can say "naoshiteimasu" or something, so while it doesn't explicitly mean "to be cured", it does mean your health is getting fixed.