Ooh we're not allowed to use such degatory terms in these PC days. "Local Authority Housing" is the preferred term!
Flat = Appartment. Flat brings visions of huge dreary 1960's concrete monstrosities. Appartment smacks of trendy design loft style urban hip living. I have friends who live in appartments who would be very offended if I told them they lived in a flat!
Counil means owned by the local authority government. Publicly owned housing is then rented out to (usually) low income tenants. Since the days of Mrs T in the 80's many council flats have been sold to their tenants who have joined the booming homeowner economy that sees a council flat in Kensington being worth £350,000 on the open market! (see last weekends SUnday Times if you don't believe me.)
Stigma still exists that Council flats and houses are the realm of the low paid and uncultured. (I hasten to add that some of my best friends live in a council house.....................)