One of the most important books I've ever read is Michael Smithson's Ignorance and Uncertainty. It gives a tour of many varieties of ignorance and uncertainty and the many strategies that have been developed in different disciplines and professional fields. Through this tour, it becomes very clear that uncertainty is not a single phenomena, and not even a couple, but instead is like a rainforest ecosystem of species. (My metaphor, not his.)
One vivid illustration of this is the taxonomy of ignorance and uncertainty. Here's the original taxonomy by Smithson in Ignorance and Uncertainty:
Smithson and his colleagues have updated their taxonomy, which is presented as Figure 24.1 in Chapter 24 "The Nature of Uncertainty" in: Smithson, M., & Bammer, G. (2012). Uncertainty and Risk: Multidisciplinary Perspectives. Routledge. (I can't find an on-line version of the diagram, sorry.) If you are looking for one book on the topic, I'd suggest this one. It's well edited and presents the concepts and practical implications very clearly.
I don't think there is one definitive taxonomy, or that having a single taxonomy is essential for researchers. I find them useful in terms of scoping my research, relating it to other research (esp. far from my field), and in selecting modeling and analysis methods that are appropriate.
Of course, there are other taxonomies and categorization schemes, including Knight's distinction between risk (i.e. uncertainty that can be quantified in probabilities) and (true) uncertainty (everything else). Other categorization you'll see is epistemic uncertainty (i.e. uncertainty in our knowledge) and aleatory uncertainty (i.e. uncertainty that is intrinsic to reality, regardless of our knowledge of it). The latter is also known as ontological uncertainty. But these simple category schemes don't really capture the richness and variety.
The main point of all this is that ignorance and uncertainty come in many and varied species. To fully embrace them (i.e. model them, analyze them, make inferences about them), you can't subsume them into a couple of categories.
[Edit: Smithson's blog is here. Though it hasn't been updated in two years, there's still some good stuff there, such as "Writing about 'Agnotology, Ignorance and Uncertainty'".]