[snugs]

We use the word for several things. Lofts to most people are the same your attics, attics tend to mean a loft converted into a room in Britain.

You also have a loft in a barn when the hay used to stored. Also we have apartments (flats) as you mention normally called loft or attic flats or apartments.

Last year I fence blew down and our neighbours put a new one up for us (we of course paid for the materials) on the left you can see our pigeon loft.
As loft can also be a building in a garden for pigeons we have a pigeon loft in our garden which is really just a large shed designed especially for pigeons.

[Tolerance Sucks Rocks]

We also use the term loft to mean storage place for hay.

More fun translations:

stove (US) = cooker (UK)
potholder (US) = oven cloth (UK)
truck (big rig) (US) = lorry (UK)