Good question. I'm working on a post on what moral uncertainty actually is (which I'll hopefully publish tomorrow), and your question has made me realise it'd be worth having a section on the matter of "risk vs (Knightian) uncertainty" in there.

Personally, I was effectively using "uncertainty" in a sense that incorporates both of the concepts you refer to, though I hadn't been thinking explicitly about the matter. (And some googling suggests academic work on moral uncertainty almost never mentions the potential distinction. When the term "moral risk" is used, it just means the subset of moral uncertainty where one may be doing something bad, rather than being set against something like Knightian uncertainty.)

This distinction is something I feel somewhat confused about, and it seems to me that confusion/disagreement about the distinction is fairly common more widely, including among LW/EA-related communities. E.g., the Wikipedia article on Knightian uncertainty says: "The difference between predictable variation and unpredictable variation is one of the fundamental issues in the philosophy of probability, and different probability interpretations treat predictable and unpredictable variation differently. The debate about the distinction has a long history."

But here are some of my current (up for debate) thoughts, which aren't meant to be authoritative or convincing. (This turned out to be a long comment, because I used writing it as a chance to try to work through these ideas, and because my thinking on this still isn't neatly crystallised, and because I'd be interested in people's thoughts, as that may inform how I discuss this matter in that other post I'm working on.)

Terms

My new favourite source on how the terms "risk" and "uncertainty" should probably (in my view) be used is this, from Ozzie Gooen. Ozzie notes the distinction/definitions you mention being common in business and finance, but then writes:

Disagreeing with these definitions are common dictionaries and large parts of science and mathematics. In the Merriam-Webster dictionary, every definition of ‘risk’ is explicitly about possible negative events, not about general things with probability distributions. (https://www.merriam-webster.com/dictionary/risk)

There is even a science explicitly called “uncertainty quantification”, but none explicitly called “risk quantification”.

This is obviously something of a mess. Some business people get confused with mathematical quantifications of uncertainty, but other people would be confused by quantifications of socially positive “risks”.

Ozzie goes on to say:

Douglas Hubbard came up with his own definitions of uncertainty and risk, which are what inspired a very similar set of definitions on Wikipedia (the discussion page specifically mentions this link).

From Wikipedia:

Uncertainty
The lack of certainty. A state of having limited knowledge where it is impossible to exactly describe the existing state, a future outcome, or more than one possible outcome.
Measurement of uncertainty
A set of possible states or outcomes where probabilities are assigned to each possible state or outcome — this also includes the application of a probability density function to continuous variables.
Risk
A state of uncertainty where some possible outcomes have an undesired effect or significant loss.
Measurement of risk
A set of measured uncertainties where some possible outcomes are losses, and the magnitudes of those losses — this also includes loss functions over continuous variables.

So according to these definitions, risk is essentially a strict subset of uncertainty.

(Douglas Hubbard is the author of How to Measure Anything, which I'd highly recommend for general concepts and ways of thinking useful across many areas. Great summary here.)

That's how I'd also want to use those terms, to minimise confusion (despite still causing it among some people from e.g. business and finance).

Concepts

But that was just a matter of what words are probably least likely to lead to conclusion. A separate point is whether I was talking about what you mean by "risk" or what you mean by "uncertainty" (i.e., "Knightian uncertainty"). I do think a distinction between these concepts "carves reality at the joints" to some extent - it points in the direction of something real and worth paying attention to - but I also (currently) think it's too binary, and can be misleading. (Again, all of this comment up for debate, and I'd be interested in people checking my thinking!)

Here's one description of the distinction (from this article):

In the case of risk, the outcome is unknown, but the probability distribution governing that outcome is known. Uncertainty, on the other hand, is characterised by both an unknown outcome and an unknown probability distribution. For risk, these chances are taken to be objective, whereas for uncertainty, they are subjective. Consider betting with a friend by rolling a die. If one rolls at least a four, one wins 30 Euros (or Pounds, Dollars, Yen, Republic Dataries, Bitcoins, etc.). If one rolls lower, one loses. If the die is unbiased, one’s decision to accept the bet is taken with the knowledge that one has a 50 per cent chance of winning and losing. This situation is characterised by risk. However, if the die has an unknown bias, the situation is characterised by uncertainty. The latter applies to all situations in which one knows that there is a chance of winning and losing but has no information on the exact distribution of these chances.”

This sort of example is common, and it seems to me that it'd make more sense to not see a difference in kind between the type of estimate/probability/uncertainty, but a difference of degree of our confidence in/basis for that estimate/probability. And this seems to be a fairly common view, at least among people using a Bayesian framework. E.g., Wikipedia states:

Bayesian approaches to probability treat it as a degree of belief and thus they do not draw a distinction between risk and a wider concept of uncertainty: they deny the existence of Knightian uncertainty. They would model uncertain probabilities with hierarchical models, i.e. where the uncertain probabilities are modelled as distributions whose parameters are themselves drawn from a higher-level distribution (hyperpriors)

And in the article on Knightian uncertainty, Wikipedia says "Taleb asserts that Knightian risk does not exist in the real world, and instead finds gradations of computable risk". I haven't read anything by Taleb and can't confirm that that's his view, but that view makes a lot of sense to me.

For example, in the typical examples, we can never really know with certainty that a coin/dice/whatever is unbiased. So it can't be the case that "the probability distribution governing that outcome is known", except in the sense of being known probabilistically, in which case it's not a totally different situation to a case of an "unknown" distribution, where we still may have some scrap of evidence or meaningful prior, and even if not, we can use some form of uninformative prior (e.g., uniform prior; it seems to me that uninformative priors are another debated topic, and my knowledge there is quite limited).

Something that seems relevant from here is a great quote from Tetlock, along the lines of (I can't remember or find his exact phrasing) lots of people claiming you can't predict x, you can't predict y, these things are simply too unforeseeable, and Tetlock deciding to make a reference class for "Things people say you can't predict", with this leading to fairly good predictions. (I think this was from Superforecasting, but it might've been Expert Political Judgement. If anyone can remember/find the quote, please let me know.)

Usefulness of a distinction

But as I said, I do think the distinction still points in the direction of something important (I'd just want it to do so in terms of quantitative degrees, rather than qualitative kinds). Holden of GiveWell (at the time) had some relevant posts that seem quite interesting and generated a lot of discussion, e.g. this and this.

One reason I think it's useful to consider our confidence in our estimates is the optimizer's curse (also discussed here). If we're choosing from a set of things based on which one we predict will be "best" (e.g., the most cost-effectiveness of a set of charities), we should expect to be disappointed, and this issue is more pronounced the more "uncertain" our estimates are (not as in "probabilities closer to 0", but as in "Probabilities we have less basis for"). (I'm not sure how directly relevant the optimizer's curse is for moral uncertainty, though. Maybe something more general like regression to the mean is more relevant.)

But I don't think issues like that mean different types/levels of uncertainty need to be treated in fundamentally different ways. We can just do things like adjusting our initial estimates downwards based on our knowledge of the optimizer's curse. Or, relatedly, model combination and adjustment, which I've had a go at for the Devon example in this Guesstimate model.

Concepts I find very helpful here are credence resilience and (relatedly) a distinction between the balance of the evidence and the weight of the evidence (explained here). These (I think) allow us to discuss the sort of thing "risk vs Knightian uncertainty" is trying to get at, but in a less binary way, and in a way that more clearly highlights how we should respond and other implications (e.g., that value of information will typically be higher when our credences are less "resilient", which I'll discuss a bit in my upcoming post on relating value of information to moral uncertainty).

Hope that wall of text (sorry!) helps clarify my current thinking on these issues. And as I said earlier, I'd be interested in people's thoughts on what I've said here, to inform how I (hopefully far more concisely) discuss this matter in my later post.