Uncertainty & Risk are 2 towers of Statistical World. Uncertainty is like dark lord sauron who could take the land underneath your feat, risk is just a evil wizard.
the statistical definitions of both are.
Risk is when we don’t know the outcome, but we know the probabilistic distribution of outcomes.
Uncertainty is when we don’t know the outcome, nor we know the distribution of outcomes.
PS:When you don’t know the outcomes, its not uncertain but its called as unknown outcomes.

Risk

Risk is always about dealing with many outcomes. A person can claim his ‘risk’ is low when the outcomes is one from the set of many. If you apply for only 1 college for graduation the your risk is high because chances of that college rejecting you is high. But if you apply for 10 colleges for graduation, risk of getting rejected from all of them is very low. In case of roll of dice you know the outcome will be one of six faces, hence its ‘risk‘ with unknown future not uncertainty.

In personal finances Risk is big player affecting the returns one gets. You carry a risk of inadequate profits if you are investor. You carry a risk of over concentration of portfolio on 1 particular industry. You carry risk of insolvency from a particular company in portfolio.

You can reduce risk by spreading your investments over a wide horizons, market caps and industries. You can reduce risk of not getting graduated by applying to lots of colleges. You can reduce risk of being single by talking to many girls about marrying. Spreading investments reduce the risk of all of them failing. Increasing options to choose reduces the risk.

Uncertainty

Often times statisticians tell uncertainty is bigger than risk. Its because uncertainty cannot be quantified reliably. Uncertainty is when you have no idea of what the future outcome will be. In case of roll of dice there is risk but not uncertainty, whereas in case applying many colleges for graduation, there is uncertainty (as no college may accept you) and risk. There will always be some uncertainty over things we don’t understand. Uncertainty exists over those conditions  where we don’t have clue about future events and where it would leave you.

The major problem one faces with uncertainty is trying to measure it (PS: Uncertainty cannot be measured). Uncertainty always exists in nature. Living beings always add some degree of uncertainty to everything they do. The question of death has uncertainty added to it, as no one knows when he is going to die.

The uncertainty is different devil and it vital lever pulling the Insurance Industry. The uncertainty of bad events makes one to have insurance. Insurance companies pool money from various people which reduces cost of insurance. But for an Insurance company you are a risk not uncertainty because, of all the customers only few of them are going to die unnaturally. The solvency ratio of an insurance company helps keep the insurance company solvent of damages caused Uncertainty.

The prudent way to deal with uncertainty is to be peaceful to it. If there exists any chances of converting uncertainty into risk for others, do it quickly. In cause of death uncertainty it can be converted into risk for insurance company by taking a term life insurance policy. The uncertainty is indication of what we don’t know, and have no goddamn clue about its working.