Hey Bud, there is no one easy way to weather an aircraft, every modeler usually has a bunch of weathering techniques in their toolbox they use depending on the kit that they are doing. For instance a WWII aircraft based in the pacific might have a different weathering approach to a modern jet fighter that spends a lot of its time indoors.
To answer your question “what is the difference between washing and weathering” well there’s not a lot of difference at all, a wash is part of the overall weathering process you do to a model.