A methodology is an approach or process to your research. It is influenced by the philosophy and reasoning behind the particular research design that you have chosen. More specifically, a methodology is the set of particular steps taken to conduct a research project. People often talk about methodologies in terms of these groups.
"Empirical work might be defined as the gathering and analysis of data from phenomena observed in the real world; it spans a range from purely observational field studies to hypothesis-driven experimentation in the laboratory."
"Theoretical work can be inspired by real-world phenomena, but it does not involve the gathering or analysis of data from those phenomena; rather, it might be defined as an exploration of what could be, rather than what is, using tools ranging from analytical models to individual-based simulations." Source: Theoretical and Empirical Perspectives in Ecology and Evolution.
Deductive reasoning works from the more general to the more specific. For example, you might start with a theory, narrow to a testable hypothesis, and observe the outcome of your experiment.
If methodology is an approach to research, then you can expect to find specific methods used to achieve that approach. Here are a couple of areas that can use different methods.
Credit:University of Maryland Libraries Research Tutorial