Method is a specific procedure or technique used to investigate a phenomenon. For example, conducting a survey, conducting an experiment, conducting a case study, etc. are methods.
Methodology refers to the general approach or framework that you use to conduct your research. For example, if you use qualitative methods, your methodology would be a particular type of qualitative research design. If you use quantitative methods, your methodology would be a type of quantitative research design.
Simply put, this is the “WHAT did the researchers use for their study” part.
Research methods include the tools, strategies, or techniques used in research. They may be questionnaires, surveys, interviews, participant observation, or other feedback surveys.
Different scientific disciplines use different methods. For example, a social science researcher might collect data through an interview, observation, auditory feedback, or survey. An ecologist might track animals for population studies; a taxonomist might count fish scales to distinguish between species; a geologist might use methods to quantify components within soil particles. In each case, the answer to the question “What did they use in the study?” refers to the methods.
The methods section of a research article usually contains information about the methods used in the particular study. This section also helps to establish a valid standard for reporting methods, which in turn helps to maintain some uniformity in science.
Simply put, this is the “HOW did the researchers conduct their study” part.
Methodology refers to the study of how research is done. It is about how we find out about procedures and the ways in which knowledge is gained. The methodology outlines the principles that guide research practice.
For example, a textbook on multivariate statistics is likely to explain the science behind how and why we use the methods it lists, and provide guidance to the researcher on how to use said quantitative techniques, where these methods are applicable, and under what circumstances they are not appropriate. Thus, the methodology explains why we use x, y, or z methods relevant to a particular research.
If we look at the etymology of the word “methodology”, it is composed of “method” and “ology”. “Ology” usually means a field of study or a branch of knowledge. So technically, “methodology” is (a combination of “ology” and “method”) a study of methods.