Ale was historically popular because it's source material (brasic grain) was extremely common.

Distillation is a relatively recent invention. We don't really see it taking off until the late middle ages. "Vodka" really is just distilled alcohol that has not been given much additional flavor via barrel aging (whisky/brandy) or infusion of herbs (gin). If you try say something like "bourbon" before the barrel aging process you might be surprised how "vodka" like it is. Its just a pure mostly flavorless and colorless liquid. This type of beverage existed in the middle ages but it was used mostly as medicine. When distilled for normal consumption, alcoholic beverages were transported in wood barrels and this added flavor and color in and of itself and wouldnt qualify as what we would know as "vodka" as a result.

Rum naturally has a bit of a distinctive flavor due to not all of the sugar cane impurities being removed but as soon as it is put in barrels and transported it also gains flavor/color and becomes non-vodka like. It was popular because wealthy europeans owned extensive slave-based plantations in the caribbean starting in the early modern time period where it was very inexpensive to grow sugarcane so there was extensive source material.