A planning permission is a permission you get if you plan to alter the shape of the roof. You submit your plan to the local council and it is open to rejection by your neighbours or the council. Without it, your loft conversion is considered illegal.
On the other hand, a permitted development means you don’t have to apply for planning permission. This is usually the case for most buildings that aren’t flats or in a designated area. Semi-detached properties are allowed an extra 50 cubic metres and terraced houses are allowed an additional 40 cubic metres.