"What is the difference between methods and methodology in research?" This question was very recently asked in LinkedIn's "Research, Methodology, and Statistics in the Social Sciences" Group, which currently has 137,052 members. A number of answers were given, including one from me. I've chosen to share mine below, preferring to start with Methodology:
In principle, the Method(s) we use in a given study is/are determined to be fit for the (stated) purpose -- the problem statement -- in terms of the Methodology or Methodologies they are couched in and, moreover, broadly accepted by the Gatekeepers (our peers and revered precursors) in our respective disciplines.
It is common knowledge that, nowadays, Methodologies and Methods cut across various disciplines and sub-disciplines.