The language was the same, it was just an alphabet that changed. Of course, each spoken language suffers changes through years and centuries, but it is a slow, permanent mutation, a kind of evolution. When you change the alphabet system, it's just a reform. Well, you can read Shakespeare with no problems, I suppose, or understand medieval English ballads - the same is with Turkish language. But the old Arabian system of letters was too complicated for common people, so when it was replaced by Latin letters, it rapidly decreased the number of illiterate people in Turkey. A simple change od "code".

Thanks Duda and NormanB, your answers have been most helpful. Good old Wilkpedia! I find it amazing that such dramatic changes can take place in the very short time in life and everyone adapts so readily.