The difference between “risk” and “danger”
The most commonly suggested synonyms for the term “risk” carry connotations that may be negative (danger, peril, threat, drawback), neutral (contingency, hazard, liability, challenge), and in only a few cases, positive (luck, fortune).
In common speech, “risky” and “dangerous” are used interchangeably, but risk is not a synonym of danger: risk is the combination of danger with a factor of uncertainty.
It is surely no coincidence that the modern notion of “risk” became widespread in France in the 17th century, historically at around the same time that the theory of probability was developed.