This diagram explains the difference well.

https://www.google.com/imgres?imgurl=https%3A%2F%2Fimage1.slideserve.com%2F1971482%2Fclimate-variability-vs-climate-change-n.jpg&imgrefurl=https%3A%2F%2Fwww.slideserve.com%2Flena%2Fclimate-change-and-natural-disasters-issues&docid=ghRrd3QwPTOhYM&tbnid=ZmB74NifmuNe_M%3A&vet=10ahUKEwiMqvHv9PDYAhUFDiwKHcTyDN8QMwhAKAMwAw..i&w=720&h=540&bih=457&biw=1024&q=climate%20change%20vs%20climate%20variability&ved=0ahUKEwiMqvHv9PDYAhUFDiwKHcTyDN8QMwhAKAMwAw&iact=mrc&uact=8

THANK YOU SO MUCH

Dear Ms Bushra

this is the best site to see your answer

https://www.pacificclimatefutures.net/en/help/climate-projections/understanding-climate-variability-and-change/

Climate - Average weather, in a wider sense is the state, including a statistical description, of the climate system.

Components of climate system - atmosphere, hydrosphere, cryosphere, land surface and biosphere. The climate system is continually changing due to the interactions between the components (internal variability) as well as external factors such as natural (volcanic eruptions or solar variations) and anthropogenic factors (changes to the atmosphere and land use).

Climate variability - deviations of climatic statistics over a given period of time (e.g. a month, season or year) when compared to long-term statistics for the same calendar period. Climate variability is measured by these deviations, which are usually termed anomalies. 

Climate change - a statistically significant variation in either the mean state of the climate or in its variability, persisting for an extended period (typically decades or longer).  The standard period is 30 years (recommended by the World Meteorological Organization).

For more information see the link:

http://www.wmo.int/pages/prog/wcp/ccl/faqs.php

Please note there are different opinions also on the understanding of the said terms - read the views of various experts across the world, the contributions related to a similar question on ResearchGate.

https://www.researchgate.net/post/Can_anyone_help_with_the_difference_between_climate_change_and_climate_variability

Best wishes

Kindly see..

http://www.miseagrant.umich.edu/downloads/climate/11-703-Climate-Variability-and-Climate-Change.pdf

Explore this too..

http://www.wmo.int/pages/prog/wcp/ccl/faqs.php

Also to see..

https://www.pacificclimatefutures.net/en/help/climate-projections/understanding-climate-variability-and-change/

See this too..

http://www.air-worldwide.com/Blog/Climate-Variability-vs--Climate-Change%E2%80%94What%E2%80%99s-the-Difference-/

Explore here too..

https://www.ncdc.noaa.gov/climate-information/climate-change-and-variability

Climate change is a confirmed tendency. Climate variations are periodic, there is not tendenciy.

Thank you all

It is very difficult to tell the difference between climate change and climate variation due to the nonlinear character of the climatic systems. For this reason it is beneficial to use the advanced spectral methods when analyzing the time series of climatic data. One of the best descriptions of the relevant techniques is given in the paper

"Advanced spectral methods for climatic time series" by M. Ghil et al.

http://www.atmos.umd.edu/~ide/data/research/publication/ssa_revgeophys02.pdf

It is also useful to apply some of ideas which were created in the the theory of dynamical systems. For the brief discussion please see the excellent presentation prepared by M. Ghil

https://climate-houches.sciencesconf.org/data/pages/ghil_1.pdf

Dr. Janusz - The attached article and the presentation are useful to understand the advanced spectral methods in the analysis of climate system. Regards

Thank you :)

Climate change is long term average...Minimum 30 years weather data set and climate variability is short term variation....It may be monthly...Seasonal or annual....Change is signal and variability is noise

Climate variability: While the climate tends to change quite slowly, that doesn’t mean we don’t experience shorter-term fluctuations on seasonal or multi-seasonal time scales. There are many things that can cause temperature, for example, to fluctuate around the average without causing the long-term average itself to change. This phenomenon is climate variability, and when scientists talk about it they are usually referring to time periods ranging from months to as many as 30 years.

Climate change: Alterations to the earth’s atmosphere that occur over much longer periods—decades to millennia—are characterized as “climate change.” While climate change can be caused by natural processes—such as volcanic activity, solar variability, plate tectonics, or shifts in the Earth’s orbit—we are usually referring to changes attributable to human activity when talking about climate change, such as increased greenhouse gas emissions. The latest (Fifth) Assessment Report from the Intergovernmental Panel on Climate Change (IPCC 2013), for example, found that on average global temperatures increased about 0.85°C from 1880 to 2012, and concluded that more than half of the observed increase in global average temperatures was caused by elevated emissions of carbon dioxide and other greenhouse gases.