Hydro-meteorological hazards vs climate extremes
The UN International Strategy for Disaster Reduction gives a good definition of a "hydrometeorological hazard": Natural processes or phenomena of atmospheric, hydrological or oceanographic nature, which may cause the loss of life or injury, property damage, social and economic disruption or environmental degradation..

The IPCC define and "Extreme weather event" as follows: "An extreme weather event is an event that is rare at a particular place and time of year".

The debate around extremes is strongly focused on extremes which are of interest to society because of their harmful effect (extreme wind, extreme heat, extreme cold, etc), but the term itself could be interpreted as having a broader meaning. We might, for instance, experience extremes of the surface pressure difference between the Azores and Iceland (a statistic which is studied by climatologist because changes in this statistic have interesting links to weather patterns in Europe) -- but this pressure difference is not usually considered as a hazard. 

An earlier answer by haresfur has given several examples of hydro-meteorological hazards which are not climate extremes. To these I would like to add:


Coastal erosion: this is a continuous process caused by tides and storms. It is hazardous for anyone living in a coastal region;
Lightning strikes: thunderstorms always pose a hazard. You could, of course, call every thunderstorm "extreme", but this is not the common usage. Thunderstorms can be common in a given region, but still be a hazard.


Hence, though the bulk of public and scientific debate occurs at the intersection of extremes and hazards, there can be hazards which are not extreme and extremes which are not hazardous.