it is not correct to say you can park in residents' bays with a blue badge.
you need to check the local rules.
my cousin got fined for parking in a residents' bay. the badge was properly displayed.
she had to pay the fine.
she was told she should have parked on a yellow line. actually there were hardly any in a small curved residential road, with multiple dropped kerbs and residents' bays.
I think my post about residents permit areas said "some areas" so it is correct. If you are going to a new area where you don't know the rules, you can usually look it up online. I have also found that the authorities are usually very understanding if you do get it wrong, so it is always worth writing to them explaining that so they can take a view.
Wouldn't it be a good idea if the rules were streamlined so all areas were the same? The rules can be very different in London Boroughs and I sometimes find it difficult to work out which one I'm in!