Traditionally although this is not the case anymore.
Council = local gov
A council estate, was social housing for plebs, although originally you needed references, to be of good moral character, families and employed where move to the front of the line.
That didn't last long.
So the new built housing, housed the poor.
The was a segregation, with bad estates have bad families and there was a stereotype that certain estate were rough ie high crime likely to be beat up.
Decent people didn't want to live in council estate.
Then labour decided to mix the poor and criminals from bad estate and mix them with good estates.
Government policy with Thatcher allowed you to buy your council house, most people didn't.
Council houses typically have lower rents, bad neighbours and free repairs from the council, ie new windows, heating, roof, insulation.
As such is a huge liability and seen as desirable to offload this housing and get money for the council.
Whereas council estates where built to house the poor, few new council estates where built as they were a liability and private housing sold at a premium.
tl;dr Council estate = public housing
Now full of feckless plebs, criminals, single mothers and paki's.
Why people say they are proud to be from an estate, just blydo working class pride.