The use of the words "risk" and "uncertainty" in vernacular English leaves the relationship between the words imprecise.
That is, if I were to ask you, dear reader, what is the difference between risk and uncertainty, there would be no univocal "right" answer, though the words clearly are not synonyms. In general, we think of risk as a less-than-certain loss, so uncertainty figures into it, but uncertainty figures into a lot of other words too (such as "hope," which we think of as a less-than-certain gain).
In finance, and in other areas as well, there has been some movement toward using the two words in a rigorously paired way, such that, to borrow a formulation from the George W. administration, "risk" represents the known unknowns of a situation, "uncertainty" represents the unknown unknowns.
Here's a straightforward example: I know that a certain stock is interest-rate sensitive. I know that the Federal Reserve is meeting tomorrow to discuss rates. I don't know what they will do in that meeting, but at least I know that I don't know. So does the market in general. Thus, the risk of an adverse decision may be said to have been priced in to the stock already today.
Uncertainty, though, under this pairing is something much woolier. The unknown unknowns. On September 10, 2001, I had no clue that Wall Street and the Pentagon would come under attack the following morning. That wasn't just an unknown like the outcome of a Federal Reserve meeting. It was an unknown unknown, and the consequences for asset values cannot be said to have been priced into anything on 9/10.
The same distinction is also helpful when one tries to think about something as personal as travel plans. Suppose I have plans that involve making a connection at an airport in Israel. Intuitively, I am fearful. I might be at that airport at a moment of terrorist attack??!?
Is my fear a reflection of a risk or of uncertainty? Another way of asking the question: can I get a handle on it quantitatively?
My thoughts on the subject today run no further, though as always I'd be happy to read the wisdom of commenters. And no, I don't have any foreign travel planned. I'm only philosophizing.