
Robert K. answered 06/02/21
Philosophy Grad Student, Experienced Writer & Teacher
The basic difference is that the first, methodological (or Cartesian) skepticism (MS), is a view about how we should go about investigating the world (or obtaining knowledge), whereas the second, external world skepticism (EWS), is a view about whether or not the external world exists.
So the fundamental tenet/claim of MS says: when we try to obtain knowledge, determine what is true about the world, and so on, we should only accept as true those claims that we can have absolutely no doubt about. In other words, if there is any reason whatsoever to doubt that some claim P is true, then we should not accept P as true. Descartes used this principle and method of MS and concluded that the only thing he could accept as true without any possibility of doubt was that he exists.
Now, the fundamental claim/tenet of EWS says: we should not believe that the external world (everything that is supposed to exist "outside of" or "beyond" my perceptions) exists. This weaker version of EWS is not a denial of the existence of the external world, but is instead a kind of agnosticism or withholding of a belief in the external world. A stronger version of EWS claims that the external world does not exist.
So, one is about a SKEPTICAL METHOD for finding truth and the other is a SKEPTICAL CLAIM about the external world beyond our perceptions. Hope this helps.