Interesting that Avis and Hertz hedge their bets in the UK by advertising "car hire and rental." In the US (and, per boronia's post, Canada as well) it's always rental. Here it's true that one hires people. Not so many years ago families who employed domestic helpers referred to them as a "hired man" or a "hired girl." (As in Robert Frost's wonderful poem "The Death of the Hired Man") These labels were commonly used in parts of New England.

In a similar vein, I wonder if the term "baby sitter" has become more or less universal. Isn't "nanny" the preferred term in the UK, or is that reserved for an ongoing arrangement? I remember when baby sitting was called "keeping house" (at least in the backwoods of NE); then in 1948 a movie called "Sitting Pretty" popularized the term baby sitter.