Risk versus Danger

The line between “risk” and “danger” is very thin, at least according to their definitions -- are either more or less real...?
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risk
n
1. the possibility of incurring misfortune or loss; hazard
2. (Business / Insurance) Insurance
a. chance of a loss or other event on which a claim may be filed
b. the type of such an event, such as fire or theft
c. the amount of the claim should such an event occur
d. a person or thing considered with respect to the characteristics that may cause an insured event to occur
at risk
a. vulnerable; likely to be lost or damaged
b. (Social Welfare) Social welfare vulnerable to personal damage, to the extent that a welfare agency might take protective responsibility
no risk Austral informal an expression of assent
take or run a risk to proceed in an action without regard to the possibility of danger involved in it
vb (tr)
1. to expose to danger or loss; hazard
2. to act in spite of the possibility of (injury or loss) to risk a fall in climbing
[from French risque, from Italian risco, from rischiare to be in peril, from Greek rhiza cliff (from the hazards of sailing along rocky coasts)]
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danger
n
1. the state of being vulnerable to injury, loss, or evil; risk
2. a person or thing that may cause injury, pain, etc.
3. Obsolete power
in danger of liable to
(Medicine)
on the danger list critically ill in hospital
[daunger power, hence power to inflict injury, from Old French dongier (from Latin dominium ownership) blended with Old French dam injury, from Latin damnum]
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Source: Free Dictionary