Planning permission
Whether you are allowed to build something at all — based on impact on neighbours, the streetscape, the local plan and planning policy. Issued by the council's planning department.
Building Control
Whether what you build meets the technical Regulations. Issued by Building Control — either the council's team or an Approved Inspector.
Why people confuse them
Both arrive in the post from the council. They are different teams, different processes, different appeal routes, and a project may need either, both, or neither.