thunderstorm; thundershower
Refers to rain accompanied by thunder and lightning; common in weather reports and forecasts.
There is a chance of thunderstorms in the afternoon.
The train was delayed by a severe thunderstorm.
A severe thunderstorm occurred in the Kanto region.
On my way home, I was suddenly caught in a thunderstorm.
There is a risk of thunderstorms this afternoon.
雷 refers to thunder or lightning itself, while 雷雨 means the rain that comes together with thunder and lightning.
豪雨 means torrentially heavy rain and does not necessarily involve thunder, unlike 雷雨 which specifically includes thunder and lightning.
thunderstorm cell
A Sino-Japanese compound of 雷, 'thunder,' and 雨, 'rain,' giving the literal sense 'thunder rain.'