Where I live, near Boston, the weather today is bad. We are having a blizzard. We have had about 20 cm. of snow so far and it is going to keep snowing until midnight. The temperature is -10°C and the wind is blowing a 40 km/hr.
The climate where I live is classified as a "humid continental climate." Its location near the coast moderates temperatures, but makes it prone to storms called "nor'easters." In January the average temperature is about 0°C.
The climate in Florida is warmer and nicer, but despite its wonderful climate, Florida can have bad weather: hurricanes, thunderstorms, and tornadoes.
(The word "weather" can, however, CAN be used to mean "climate." Song lyrics say:
"I'm going where the sun keeps shining
Through the pouring rain
Going to where the weather suits my clothes..."
The lyricist, Nilsson, could have used either the word "weather" or "climate" but chose to use "weather.")