Outside the U.S., there is no difference between flyer and flier. They are interchangeable, though flyer is about twice as common as flier. American writers tend to use flyer for small handbills and flier for people and things that fly. This distinction does not run deep, though, and the two spellings are very often used interchangeably even in the U.S., so it’s safe to say that neither is correct or incorrect for any sense of the word.
An earlier version of this post said simply that flier is the American spelling for all senses of the word while flyer is preferred everywhere else. This is the conventional wisdom, but it’s not consistently borne out in practice.
There is little consistency in spelling of the word outside the U.S. The Guardian style book, for example, says “flyer, not flier,” while the Daily Telegraph style book says “flier, not flyer,” but in practice these newspapers and other non-U.S. publications use both spellings seemingly with no pattern except that flyer is more common. Obviously there is no agreement on the issue, and the flier–flyer distinction is unsettled for now.
American publications tend to use use flier for someone who flies and flyer for a small handbill, as in these examples:
American Airlines introduced the first of what we now know as frequent flier programs in May 1981, with 283,000 members. [USA Today]
According to the flyer—which depicts a raised, clenched fist holding a pencil, a play on the movement’s symbol—Duggan plans to bring in guest speakers. [Wall Street Journal]
The infrequent flier about to get on the plane at Reno-Tahoe International Airport had sores all over him. [Los Angeles Times]
“Join us as we revisit a familiar and beloved neighborhood of the Christmas Tour,” a flyer for the event says. [Boston Globe]
Again, though, this is just a tendency and not a rule, and we could find plenty of counterexamples.
Outside the U.S., flyer is more common for all senses of the word—for example:
Something of his alert oversight probably came from his experience as a flyer. [Guardian (U.K.)]
Once inside a store, look for items that are on the outside cover of the weekly specials flyer. [Globe and Mail (Canada)]
Elected just 18 months ago, already a high-flyer. [Telegraph]
They must also stop distributing or displaying any literature, flyers or signage containing any unregistered business name. [Sydney Morning Herald]