Hazard is commonly used in a narrower, more specific sense. You can normally identify a hazard (threat, source of danger), and use of the word might be encountered in some settings more than others. For example, petrochemical refineries might store hazardous chemicals like H2SO4. Or while driving on a mountain road you might observe signs that call your attention to the hazard of rockslides. I think hazard is more often used when there is a risk to your (or the public's) safety.
Risk is a far more general term. Hazards are risks of a kind, but not all risks may be called hazards. While it is a risk of driving on a mountain road that your car may be struck by falling rocks in a rockslide, it is also a risk that you run out of gasoline or petrol, becoming stranded. Running out of gas is a risk, but not a hazard. A risk is an unwanted outcome, usually something you want to avoid or plan to prevent. Insurance carriers offer insurance against risks (auto collision, fire, hospital care, etc.), businesses manage risks (what if our product isn't ready for the Christmas sales season, or our film goes over-budget?), and entrepreneurs take risks (is it a good time to start a locksmith shop in this city?).