These two terms can sometimes be used interchangeably, but actually have slightly different meanings.
A hazard is the possibility of something causing harm
A risk is the probability and likelihood of harm occurring.
For example, it’s possible that a bottle of bleach could be used incorrectly, causing harm. But you need to ask, how probable is it that this is going to happen? Until an action has actually occurred, it is only a hazard, not a risk.
Another example could be working at heights. Standing on top of a tall building is a hazard. The risk is how probable (say high, medium or low) will you slip or step off the building and cause harm to yourself.
You should care because managing your hazards and your risks all help to prevent incidents and injuries. That is what your health and safety systems are all about.