The difference between Climate-Weather is really a measure of time. Weather is what happens over a short time, and Climate is the behaviour of the atmosphere over a longer period.
The clouds you see above were photographed on the east coast of Australia, and indicate what the conditions were like on that day, and on that part of the coast. Weather is the specific condition of the atmosphere at a particular place and time. Things like wind speed and direction, temperature, humidity, atmospheric pressure, cloudiness, and precipitation are used to measure the weather. In many locations it can alter by the hour, each day, and varies with the seasons.
“Climate change refers to the variation at a global or regional level over time. It describes the variability or average state of the atmosphere or average weather over time scales ranging from decades to millions of years. These variations may come from processes internal to the Earth, be driven by external forces (e.g. variations in sunlight intensity) or, most recently, be caused by human activities” Wikipedia.
The two terms are certainly linked, but climate is the average of weather conditions over significantly longer periods of time.