Planning permission is mainly concerned with the site layout, external design and the effect of the development on the environment and neighbouring properties.
The Building Regulations are concerned with the actual construction process for both internal and external alterations, and involves regular site inspections whilst the works are in progress. This includes checking the structural stability, fire precautions and means of escape, weather resistance, energy conservation, sound insulation, access and facilities for disabled people.
Some (though not all) types of works may require both approvals, and some may need one or the other. Both are completely independent of each other.