Landslide is a more general term than mudflow. It refers to the gravity-driven failure and subsequent movement downslope of any types of surface movement of soil, rock, or other debris. The term incorporates earth slides, rock falls, debris flows, and mudslides, amongst other categories of hillslope mass movements. They do not have to be as fluid as a mudflow.
Mudflows can be caused by unusually heavy rains or a sudden thaw. They consist mainly of mud and water plus fragments of rock and other debris, so they often behave like floods. They can move houses off their foundations or bury a place within minutes because of incredibly strong currents.