I do not claim to be an expert, but my understanding is this.
Sugar cane is the raw ingredient for all Rum.
However, there are various extraction processes between sugar cane and 'sugar' which produce various byproducts, one of which is molasses (basically the high color, high sweetness, high protein, soluble fraction of the juice extract which is separated from the crystalline sugar stream).
You can either use the 'whole' pressed sugar cane juice for rum, including the fraction that could be refined into sugar, or you can first process the cane, extract the sugar, then use the molasses. Molasses is cheaper.
I don't think one is necessarily any better than the other from a taste and quality perspective, considering that the yeast will clear up most of the fermentable carbs and protein anyway, then distillation will clear the rest, but that's a point of differentiation that some brands use as a 'quality marker'.