A correlation doesn't necessarily mean that one occurrence is caused by the other.
For example there is a correlation between the consumption of organic foods and autism. However these occurrences are completely unrelated. Therefore this correlation cannot prove any relationship between the two subjects.
However, there is evidence that smoking does cause lung cancer. Smoking causes over a quarter (28 per cent) of cancer deaths in the UK.
Cancer is caused when smoke particles damages our DNA. Many of the chemicals found in cigarettes have been shown to cause DNA damage, including benzene, polonium-210, benzo(a)pyrene and nitrosamines. Since the DNA is damaged, the genes responsible for cell division can mutate. Cells can start to divide uncontrollably as they will not respond to apoptosis, which would lead to the formation of tumours and cause death.
http://www.cancerresearchuk.org/about-cancer/causes-of-cancer/smoking-and-cancer/smoking-facts-and-evidence#smoking_facts0
http://www.buzzfeed.com/kjh2110/the-10-most-bizarre-correlations#.wtwJ0xo0Ep