The difference between expository and argumentative writing, if you'll allow me to follow Habermas' "Theory of Communicative Action", is that argumentation is a form of exposition that limits itself to a particular reasoning mode. Habermas lays out four basic reasoning action modes (and please forgive the exhaustive descriptions):
- Teleological action: Reasoning here involves nothing except the pursuit of goals by effective means. Thus if I (say) want to buy a new car, I will list out the things that need to happen in order for that new car to be bought, and plan out the steps I need to take to make those things happen. Most often we want to deal with the subset of teleological action that involves engaging other people (what Habermas calls 'strategic action'); in other words, we don't just plan out our own goal-oriented actions, but work with, manipulate, predict, or accommodate for the actions of others.
- Normatively regulated action: In this mode, reasoning assumes and subsumes group-specific norms and standards as pre-given facts. This mode is often obvious in conservative groups (religious or secular) which hold certain values and structures as sacrosanct, though clearly it appears in many contexts. There's always a tension between normatively regulated action and pure teleological action, since moral norms often preclude simple and effective means of achieving goals.
- Dramaturgical action: This kind of reasoning is focused on the creation and preservation (or at times the destruction) of a persona that reflects a high-value image within a group. What that image might be can vary. We might think about conspicuous consumption, which goes beyond the goal of consuming any particular thing to create a persona that seems capable of consuming everything; or perhaps we could consider sanctimonious behavior in religion, where someone ostentatiously displays symbols of devoutness, acts of charity, expressions of righteousness, and such, in order to be seen in the community as a paragon. And of course, this also appears in perverse forms, where people try to bolster their own persona by ripping at the personas of others, tearing down what they cannot rise above.
- Communicative action: In this mode, reasoning revolves around the effort to achieve consensus, even if it comes at a cost to specific goals, norms, or persona identifications. The prototype here is the idealized scientific method, where researchers seek mutual agreement about theories by testing them against mutually observable events: beliefs, egos, and personal goals notwithstanding. But of course, communicative action also lies behind most philosophical thought, and lurks in the idealizations of democratic theory.
When we write in an expository form, we might use any or all of these modes as we try to persuade or inform the reader. For simple explanatory pieces we probably never get out of teleological mode: the goal is understanding; these are the pieces of knowledge required to reach that goal; these are the steps we need to take to transmit those pieces of knowledge. For more persuasive work we might find ourselves invoking strategy (e.g., "If you approach it this way you'll get better results"), or norms (e.g., "That kind of thing is not what we do in America"), or dramaturgy (e.g., "If one is sincere about this, one would naturally do that"). We might even invoke communicative action (e.g., "There is a common ground we can find if we work for it").
However, when we write in an argumentative (analytical, scientific) mode, we are invariably involved with communicative action. A research paper might seem (superficially) like an authoritative declaration, but in truth a research paper is asking readers to agree with a certain proposition based solely on the evidence it lays out and curates. The other modes of reasoning are actively discouraged in formal research. Even though a research article may seem simply explanatory, it is still arguing for a case: in your example, it would be arguing that these are in reality the side effects of that pill, as demonstrated by the study undertaken.
The question of a thesis statement is a bit of red herring. Technically speaking, yes: all expository and argumentative writing has a thesis statement. But in many cases this thesis statement is transparently trivial. If I write an exposition on wildfires then my thesis statement might be something as mindless as "This is how wildfires work," which may not even be worth mentioning in the course of the exposition. Likewise, research skills are always useful in expository or argumentative writing, but here we have to distinguish between two skill sets:
- 'literature review' skills, in which we seek out, evaluate, and incorporate other writing into our own, and...
- analytical skills, where we design research, draw out and formalize evidence, categorize and structure results...
The first is useful in all expository and argumentative writing, the second not so much. We would hardly need to develop an entire research paradigm of our own to write an expository essay persuading people to (say) get the Covid vaccine.
Of course, this doesn't quite fit with your division between argumentation and exposition; I've made things more complex, as is my (un)fortunate habit. But I think seeing argumentative writing as a restricted form of exposition in this way might help you structure how you lay out your classes.