Here is what AHD has to say on the matter.
rent[sup]1[/sup]
n.
1. a. Payment, usually of an amount fixed by contract, made by a tenant at specified intervals in return for the right to occupy or use the property of another. b. A similar payment made for the use of a facility, equipment, or service provided by another.
2. The return derived from cultivated or improved land after deduction of all production costs.
3. The revenue yielded by a piece of land in excess of that yielded by the poorest or least favorably located land under equal market conditions. Also called economic rent.
v. rent·ed, rent·ing, rents
v. tr.
1. To obtain occupancy or use of (another’s property) in return for regular payments.
2. To grant temporary occupancy or use of (one’s own property or a service) in return for regular payments: rents out TV sets.
v. intr.
To be for rent: The cottage rents for $1,200 a month.
Idiom:
for rent
Available for use or service in return for payment.
[Middle English rente, from Old French, from Vulgar Latin *rendita, from feminine past participle of *rendere, to yield, return ; see render.]
renta·bili·ty n.
renta·ble adj.
hire
v. hired, hir·ing, hires
v. tr.
1. a. To engage the services of (a person) for a fee; employ: hired a new clerk. b. To engage the temporary use of for a fee; rent: hire a car for the day.
2. To grant the services of or the temporary use of for a fee: hired himself out as a cook; hired out the cottage for the summer.
v. intr.
To obtain work: She hired on as a deck hand. He hired out as a photographer.
n.
1. a. The act of hiring. b. The condition or fact of being hired.
2. a. Payment for services; wages. b. Payment for the use of something.
3. Informal One who is hired: two new hires in the sales department.
[Middle English hiren, from Old English hýrian.]
hira·ble or hirea·ble adj.
hirer n.
In general, I use ‘rent’ for buildings and ‘hire’ for people and things. It is very unusual in British English to use the word ‘hire’ as a noun.
When used as a transitive verb, I can see a slight distinction upon the lines of ‘lend’/‘borrow’ and ‘teach’/‘learn’.
"Bill lent Ben ten euros."/"Ben borrowed ten euros from Bill."
"Bill taught Ben how to ride a bike."/"Ben learnt how to ride a bike form Bill."
"Bill rented a pogo stick to Ben."/"Ben hired a pogo stick from Bill."
- ‘Boing’ said Garzo.