They were definitely made for a British audience (were they even released in the US?) but yes they were quite different, although based on the first two TV Dalek serials.
Cushing played Dr. Who, a (human) scientist who had invented a time machine called Tardis in his backyard. It was bigger on the inside - but only a little, and filled with all sorts of crazy wires and contraptions. Dr Who and his granddaughters, Barbara and little Susan, got sent flying through time when Barbara’s bumbling boyfriend, Ian, accidentally activates the controls of Tardis and they wind up on the planet Skaro, confronting some very colourful Daleks.
In the second movie, Dr Who, his niece Louise, and little Susan meet Police Constable Tom Campbell (played by Bernard Cribbins, who would go on to play future companion Wilfred Mott alongside David Tennant and Catherine Tate) after he runs into Tardis, thinking it to be a real police box, before heading off to meet the Daleks in 22nd Century Earth. Although based on the Doctor Who serial ‘The Dalek Invasion of Earth’, this time Dr Who does not abandon his granddaughter Susan against her will at the end of the story.