Climate classifies what type of weather an area will typically have. For example, Miami summers are typically very warm and humid and often see daytime thunderstorms. Typically, 30 YEARS of weather data is needed to establish climate data.
Weather is what meteorological conditions have recently or are currently occurring.
Permanent and semi-permanent air-masses dictate climate. Whereas, weather is dictated by both semi-permanent air mass AND migratory influences - like troughs, ridges, fronts. In addition, weather is also dictated by "diurnal" influences. These are changes in the atmosphere from day to night with the gain and loss of the sun's heat.
Climatology is a whole separate realm of meteorology from "weather forecasting".