A flat can be an apartment. The real difference is that an apartment can also be one residence in a building of many - that each floor (ie given there are 5 floors for example) contain 2 or more apartments or separate residences. However, a flat is one residence that occupies one entire floor. If there is a building with 5 floors and each floor is only one apartment/ 1 separate residence that building is a flat. the single apartments are piled one on top of the other creating a flat formation of apartments

For the kind of accommodation you are describing, speakers of variations of British English would usually say 'flat', and speakers of variations of North American English would usually say 'apartment'. It's interesting to read Gary's answer. Here in the UK, a room in a shared house would not be called a flat, and here, a flat doesn't have to be a single bedroom unit either, but can have a bedroom and a lounge, two bedrooms and a lounge, etc. If it is just one room with cooking and bathing/showering facilities, then it is called a studio. If it is just one room with a private kitchen but a shared bathroom, then it is called a bedsit.

yes, simple explanation is- flat-british English, apartment-american English.We could call the place you are describing as a block of flats.Cheers Kamila

Thank you all for your answers!

Yes, in most basic terms, Americans live in apartments. People in the UK live in flats. The difference is a difference between American English and British English. But, as others have explained, the uses of the words can get more complicated than that.