Legally, only elected councillors can be paid. Co-opted councillors cannot be paid.
In most cases councillors are unpaid, however there may a Chairman's allowance (ours is £300pa), and all councillors, irrespective of elected or co-opted may claim legitimate expenses.
If any Councillor (not the Chair) is paid, all, elected councillors must be paid the same.
The council can choose to pay the Chair and not other councillors. In this case a co-opted Councillor as Chair can be paid, but this stops when they stand down.
But in most cases and most councils councillors are unpaid.