>you rent things, but hire people
Funny, I would never hire a person, only recruit or employ them, although I might use the term "hire and fire" just because of the way it sounds. I have also seen occasional signs on windows (maybe McDonalds) saying "we're hiring" and people would understand it. Maybe that is where the main difference lies, because we do not, in general, use hire for people we do not need to use replace the term with rent when referring to things.
In running a course for management boards of voluntary organisations we used to say that the main role of the board was to hire and fire the chief executive. Sadly one useful North American philosophy for boards of voluntary organisations never really crossed the pond - "give, get or get off".
I would:
* recruit (possibly using a recruitment agency), employ, contract or "take on" a person
* hire (short term) or lease (longer term) a car (although I see that companies such as Avis and Hertz use the term "car hire and rental" to hedge their bets) - also hire: tools, clothes, bikes almost anything
* rent or lease a flat
