Depending on the program you're in and the orientation you plan to adopt in your own research, I'd say don't get too hung up on the distinction because often there isn't one! Postmodernism, for example, is both a methodology and a theory. It is a theory that critiques modernity, objectivity, rationality, etc, but that in itself is a methodology because it allows you to read primary sources through a different lens, one that purports to let you uncover new meanings, intentions, structures of power and meaning etc.

I would simply define methodology as the set of tools you use to analyze the past.

I think too many professors assume that students know these things, and graduate students in particular don’t like to ask these ostensibly simple questions that are actually fundamental and far from simple for fear of looking like an imposter. Mind you, in my experience a lot of professors haven’t given this much thought themselves. The empirically oriented ones tend to ignore the theoretical and historiographical underpinnings of how we do what we do, when in fact we’re all engaging with methodology whether we’re aware of it or not.