What is the difference between a filler word and a discourse marker?

Discourse markers are really just a catch all term for all the different lexical ways of making text (discourse) hold together beyond the level of the clause. As all linguistic categories (including nouns and verbs) the discourse marker category has fuzzy boundaries and is subject to prototype effects, family resemblances (and the like) - sort of like Lakoff's radial categories. Which is why it is hard to find an easy definition that would include all the things that look like discourse markers and exclude those that don't. But ultimately it's not all that important. What's important is that all those little words that are hard to categorize play an important role.

Words that are often called 'fillers' (like, so, uhm, etc.) are a type of discourse marker that is used to manage attention, conversation turn taking, or just the flow of the speakers speech, work together with intonation and other non-segmental elements. Whether you call them fillers, discourse markers or something else is less important than it is to recognize the role they play in speech or writing.