All weather is weather. But there can be varying degrees of weather-related events. For example, high winds, storms, tornadoes, etc. can be termed "wild weather".
"Wild weather" basically describes instances where the weather has turned up to be completely unpredicted or in a force that was larger than predicted, such as freak lightning storms, earthquakes,...
Weather is the condition of the atmosphere at a given time in a certain place whereas climate is the condition at the certain place year round. In other words , if you live in a place like Florida ,...