Can a Brit fill me in on what exactly a "flat" is? I know it means something like an apartment but I'm not sure exactly, and honestly when I saw the words "the flat" I thought the sentence was referring to, like, a salt flat until I saw "on the ninth floor" and remembered, "oh yeah, that's a British thing". :P
We would usually always call a flat an apartment. Though sometimes (but not always) apartment has a "rental" subtext that flat does not share, and is maybe more like condo.
Confusingly, apartment is also used in British English, but differently; I think every British apartment is a flat, but not every flat is a British apartment.
I agree that flat is not a good translation of lakás into American English, but is a good translation into British English.
A flat is a rented place to live, It can be like an apartment but that implies being upscale. It can also be a share of an ordinary house. As a student I went "flatting" ie a group of us got together and shared the cost of a single house - and I mean house - usually old wooden bungalows with big rambling gardens.
Maybe both sides of the Atlantic use the same words but they have different meanings. A "flat" is always rented and maybe in a block of connected houses, a tower block, or a standalone house (bungalow). An "apartment" is never standalone and is in a building with other apartments. And apartment may be owned or rented.
To stir it up, maybe we could also include the meaning of the Hungarian "apartman" :)
It is basically a separate, (semi-)independent part of a larger structure, which can be used as living quarters separately from the rest of the building. It could be
- a wing of a house,
- the part of your manor that you designated for the use of your mother-in-law,
- what they call a "suite" in US hotels (as opposed to a simple "room")
- a large, luxury apartment in a high-end building (with doorman, indoor pool, river-view, etc.)
- or a vacation rental apartment (as opposed to a room), with its own kitchen and bathroom, maybe several rooms)
For other purposes, Hungarians mostly use "lakás", which can be qualified as
"bérlakás" - rental apartment
"öröklakás" - yours "forever", ie. you own it. I guess this term is not much used anymore when this is the default. It made more sense a few decades ago, when a large quantity (maybe the majority) of apartments was goverment-owned, and people were renters, paying rent to the goverment.
There are other terms, as well, but the basic common word is "lakás".
To further mix it up, in Turkish, the word "apartman" means a whole apartment building/complex, not the individual flats/apartments.
From my English - flats can be rented or owned.
For example, you can have a "granny flat" - which is a self-contained unit off or part of a larger house.
So, you are right - it really depends on the definition of "flat" that exists in your mind due to common usage around you.
Maybe apartment would be a better "default" translation with other variants (such as "flat") being included.