For indicating the history of not far and early past (for example until a century ago) which one describes better? contemporary history or recent history?
"Contemporary history refers to the history of events usually within the lifetime of the historian, although sometimes, in the European or North American context, to post-1945 or even post-1914 history."
That said, if you are having a normal conversation, most people would use "Recent History". "Contemporary History" is for more formal situations, like defending your doctoral dissertation.