The terms framework and methodology are sometimes used interchangeably, but they are not the same thing. I’ll briefly discuss the differences by providing basic definitions.
A methodology is a description of how to do something that includes specific steps to reaching a goal or goals. It is detailed, specific and prescriptive. A framework does not have steps, whereas a methodology does. A framework is intended to be flexible. You would take the framework and adopt it to your situation. A framework is a skeletal structure around which solutions are built.
A framework is a flexible, incomplete structure that allows for other tools and practices to be inserted where appropriate. A framework is structure for classifying and organizing complex information. A framework is a model or a simplification of a complex thing that guides you through your decision-making process. It alerts you to areas of consideration and importance. It’s a general guideline that does not specifically tell you what to do, other than to consider the specified aspects or components.
With a framework, you only select those parts of the framework that you need, and leave the other parts out, as you wish.
Which one is the proper word to use, a framework or methodology? The answer is that it depends on the context and the goals of the project.
The indeed career guide has an article called Framework vs. Methodology: Differences Between the Two.
Here’s an article at Think Insights called What Is The Difference Between A Methodology And A Framework?
Note that Agile is not a framework or a methodology.