Rum is a complex subject. There are hundreds available commercially in the United States and thousands worldwide.
Here are a few facts to help you figure what ‘s in that bottle you are holding:
Rum is a distilled product made from sugar cane. One type is made from sugar cane juice directly (Rhum Agricole) and others are made from molasses – a byproduct of sugar production (Rhum Industriel).
Rhum Agricole tends to be a less highly distilled product with more flavors as a result, Rhum Industriel is generally distilled to a higher proof to lose the flavors molasses can impart.
Either type can be distilled in a pot or column still the vast majority being made in column still for cost/speed reasons.
White rum is usually straight from the pipe (unaged), and usually used in mixed drinks. Other rums are aged anywhere from 6 months to (supposedly at least) 25 years. Reposado (rested) means 3-6 months aging, Anejo (aged) means at least one year. Gold is a meaningless term meaning colored with caramel usually.
Geography: For purists the designation ‘rum’ is only considered for rum coming from the Caribbean. For others it means any sugar cane based spirit no matter where it is produced. In the Caribbean rum varies widely in style and taste from island to island and within each island distiller to distiller. See also Aquadiente and Cachaca. For true enthusiasts, check out Ed Hamilton’s website: www.ministryofrum.com it is THE Rum Website.    
Flavored or infused rum is even more complex subject.
Flavored – A somewhat slippery term- strictly speaking it of course means the rum is flavored – how is the big question.
Flavored unless another term is also used or specified means (usually) that someone blended in a flavor, extract, chemical equivalent thereof, etc to the rum. There is a substantial variation in quality/palatability in these rums – they tend to be grim. At best they taste like some candy/ice cream etc., not a real drink. They are aimed at the young ( O.K. lets be frank – underage or barely legal crowd) -not quality stuff.
Infused – Usually means they used some real ingredients at some point – either soaked in the rum directly or were added to the rum during the distillation process