Rum, Rhum, Ron, Cachaca, Aguardiente... The Rum family is a large one. The only thing you can say they have in common is their ancestry. They are all descended from Great Granpa Sugar Cane in one way or another. Sugarcane juice, sugar cane syrup, or molasses (which is a by product of cane sugar manufacturing) are the only things that rum may be made from.
Rum first came about back in the days soon after the discovery of the Americas. Sugar cane was imported and planted and the processing of sugar from its juices began. Molasses, a byproduct of sugar manufacturing was either thrown away or used as fertilizer when some slaves drank some of the waste molasses that had been sitting in the sun and rain for a few weeks ad had fermented into a sweet/sour 'beer' that was highly flavored but only mildly alcoholic. first only slaves drank this crude 'rum beer' but it came to the attention of the plantation owners and soon they started playing around with distilling it and rum was born. By 1651 it was already in widespread production and documents from Barbados, what may be the home of rum, show that 'rumbullion' aka 'kill devill' as it was known, was a fiery and cheap spirit.
Over the years rum came to be made wherever sugar cane was processed into sugar. Every sugar cane plantation also became a rum distillery as a way to make money off of the waste products. Soon more care was used during the process and fine rums were being made. The high temperatures, fast fermentation, long aging in barrels, and other factors of the tropics made rum become a spirit unique from any others being produced. The intense flavors were so different from the other spirits of the time like cognac, fuller and sweeter.