Vague and ambiguous are buddies. They are often used together, and people use them interchangeably. But while something can be both vague and ambiguous, the two are not synonyms:
- Vague means unclear, or imprecise.
- Ambiguous means capable of having at least 2 meanings.
I’m not sure when it happened, but “disinterested” has come to mean the same thing as “uninterested.” Oddly, at least according to this, that was what it originally meant anyways. This is wild speculation, but I think that at least some of the shift comes from a sense that people have that the prefix dis- is more powerful or makes you sound smarter than the prefix un- (dis- is from Latin, while un- is from Middle English*).
I don’t really care about whether one meaning for “disinterested” is right, or whether using it to mean “uninterested” is a mistake, but I will point out that it is a useful distinction to keep in mind. You might want a disinterested reader, but you almost definitely don’t want an uninterested one.
* “Bad writers, and especially scientific, political, and sociological writers, are nearly always haunted by the notion that Latin or Greek words are grander than Saxon ones…” -George Orwell, Politics and the English Language.