A flat, similar to an apartment, is a housing unit that's self-contained but is part of a larger building with several units.
While the words apartment and flat are often used interchangeably, some people refer to single-storied units as flats because of their "flat" nature. The term flat is most commonly used in the UK, where in North America a similar unit will more likely be referred to as an apartment.
Although the terms differ, "flat" and "apartment" are generally used interchangeably when they're used in the U.S. The biggest difference between them is that "flat" is used most commonly in the U.K., and "apartment" is used in North America and the United States. In the U.K., if a unit is two or more stories, it may be referred to as an apartment. Units with single stories are considered flats.
Some areas of the world are more likely to refer to a unit within a building specifically built for residency as an apartment, whereas a unit in a building originally for a different purpose that was converted into a living space would be considered a flat. For this reason, many people associate flats with older buildings that often have more character than a new, cookie-cutter development.
If you're in the market for a charming, single-storied living space, a flat might suit you well. If you're living outside of the United States, your flat apartment search might be more varied in type than it would be in the U.S.