Attack Types and Stats

Hi all, do the attack type descriptions (dash, down arrow, equals, up arrow) (None, Poor, Fair, Great) directly affect the visible stats of your weapon or are they an invisible modifier?

The main reason I'm confused is by equipping a slightly heavier blade, my stab goes from "fair" to "poor" (because the heavier blade is meant more for slash) but my damage goes up? My Attack Abilities have the same scaling too, so I was wondering if the attack type wasn't as big of a deal as thought it would be, or if it only comes into play when considering the enemies' resistances too?

https://preview.redd.it/5icysgvljjfd1.png?width=2560&format=png&auto=webp&s=089acd3f458ee22ba0bffda14ec95eb44bc7b149