The Def Leppard song "Pour Some Sugar On Me" is an iconic rock anthem from the 1980s, and it's one of my favorite tunes from the group. The song has nothing to do with sugar or sugar cane, but three spirits are derived from sugar cane -- rum, rhum agricole, and cachaça. You've definitely heard of the first one, you probably haven't heard of the second one, and you might have heard of the third one. If you're familiar with all three, then congrats.
So if all of these spirits come from sugar cane, what are the differences? And why should you care? This short article from Tara Nurin at Vinepair has an excellent summary. Let me distill (pun intended) the technical stuff down to the basics. Rum comes from fermented sugar cane juice or molasses, which is a byproduct of the refining process. Rhum agricole only comes from pressed sugar cane juice that is not fermented. Cachaça is a cross between the two, as it must be fermented (like rum) but only can come from sugar cane juice and not molasses (like rum agricole). Rum can come from anywhere (not just the Caribbean), rhum agricole is associated with French Caribbean territories (agricole means agricultural in French, and that's why it uses the French spelling of rhum), and cachaça is the national spirit of Brazil.
Rum in and of itself is a big category, so I encourage you to explore different brands and ages. When you read descriptions of rhum agricole and cachaça, you'll probably see words like earthier, vegetal, and funkier (George Clinton or Prince would approve -- get it?). Those are pretty accurate. The bottom line is you can have a lot of fun experimenting with these related spirits in your cocktails.
With apologies to the guys from Def Leppard -- step inside, cocktail this way, you and me (sugar) cane, hey hey!