Standard is the best practice that has been tested and implemented with in the industry while a methodology can be thought of as PMI's well designed framework or documented procedure in applying Project Management. Saving Changes...
PMBOK Guide (Standard) + Adaptation for your Organization = PM Methodology for your Organization
Standard= a set of collection of rules or guidelines in accordance to best practices (example PMBOK 6th Ed)
Methodology= A methodology is a set of ideas or processes or procedures have been applied in some organizations and becomes a methodology for their future projects.
For example (An organization applied a set of ideas/processes/procedures/templates to by used by their PMs - Such methodologies used to be created by PMO.
"Methodology" is one of the more abused terms in project management. Literally, but rarely used, "methodology" is the analysis of different methods that can be used. We see this frequently in this community, when we're discussing and debating different PM practices, but we rarely use "methodology" in that sense.
In more generally use, a "methodology" is the set of practices that an organization has adopted. Your workplace might have a PM methodology. I don't think I'd refer to the PMBOK as a methodology, as it more describes good practices but doesn't define how you should do your job. You'll commonly see the phrase "Agile methodology," which is incorrect ("Agile" is more properly defined as a set of values and principles, not a method).
Commonly but incorrectly, you'll hear people use "methodology" to describe a specific practice they use. It's often used as a fancy way of simply saying "method." Saving Changes...