This is a yes/no kind of question and you can answer to this with:
- Kyllä, osaan piirtää ja/tai maalata.
- Ei, en osaa piirtää. / ...en osaa maalata. / ...en osaa piirtää enkä maalata.
In this question you can't use "vai" at all, but in other types of questions the difference is:
- "Piirrätkö tai maalaatko?" For example, if I'm having a conversation, I ask this question to learn if they ever draw or paint overall. To this one they can answer "kyllä" or "ei", just like in the examples above.
- "Piirrätkö vai maalaatko?" For example, if I see someone working on something but I can't see whether they are drawing or painting, so I ask this and to this one they can't answer yes or no, but they are going to answer with verb or so, e.g. "Piirrän." or "Maalaan."
Hm... but just one - artificial - situation. Just in case my friends talks a lot and I didn't get him right because I did not listen well, could I ask then "osaatko piirtaa vai maalata?" in the sense of "so do you know how to draw OR to paint?" - in this case its not Yes/No but a decision. Would it be correct then, or still tai ?
If you know English: it's pretty much like when English uses a rising tone for yes-no questions (which tai in Finnish does) while it uses a falling tone for choice questions (except yes-no questions) and all other questions (like the ones with what, where, etcetera) (which vai in Finnish implies).
Ja, it is over sensitive because the English "can" doesn't differ strict enough between the possibility and expertise. But that shouldn't lead to artificial solutions, instead, they could explain it because the difference between possibility and expertise is not unique in Finnish