The distinction is based on their ingredients, with agricole rum being made from the crushed sugar cane itself, whereas most rums are made from molasses a by product of processing cane for sugar.
You'll find the French Caribbean islands are the main sources of agricole rum, and I believe this is due to the similarities between using this "cane juice" and using grapes to make cognac.
agricole rums tend to have lighter fruity notes to them, but of course they can be rich too
Off the top of my head I don't believe any of the rums you've mentioned are agricole except (kind of but not officially) zacapa