The Russian word 'мир' is derived from the Proto-Slavic 'mirъ', which in turn is derived from Proto-Indo-European (PTE), which was a spoken language from about 4500 BCE to 2500 BCE. Given that the word has therefore been around for at least 6500 years it's pobably not unsurprising that it's been used in more than one way. Indeed, the original word had become 'mitis' (meaning 'mild') by the time it found its way into Latin (which, like modern Slavic languages, can also be traced back to PIE).
As has been suggested above, context will help a Russian speaker to understand which of the two meanings applies when he encounters 'мир'. For example, 'Война и мир' is usually seen as meaning 'War and Peace', rather than as 'War and the World' (which could be a possible interpretation, as the Slavic group of languages doesn't make use of definite or indefinite articles), simply because 'peace' is an antonym of 'war'.