Mohammedan
Both the correct and a supposedly-archaic term for "Muslim", "Mohammedan" simply means "follower of Mohammed", since one can be a "Muslim" (submitter) or in "Islam" (submission) to anyone to anything.
Therefore, since one can be a "Muslim" (submitter) or in "Islam" (submission) to anything, the term "Mohammedan" would more correctly apply to "Muslims".
Orthodox Mohammedan
Often mistaken for a "radical" or "extremist" "Islamist", an Orthodox Mohammedan is one who carefully observes and follows the tenants of Mohammedism ("Islam"), including Anti Semitism and jihad.
Looking at Mohammed's life, one will see that a "radical Islamist" is actually an Orthodox Mohammedan.