say that a sword have 20 dmg, and a mace have 20 dmg. Swords hit faster than than maces, does the sword still do more dmg?
I think what you mean to be asking here is "is the listed damage the damage per hit or the DPS?". It's the damage per hit. Given a 20-dmg sword and a 20-dmg mace and assuming an unarmored target and no weapon perks, the sword will do more damage in a given amount of time because it will get more hits in. (But note that, for any given tier of weapons, the mace will have a higher damage per hit - e.g., a steel mace has a higher damage than a steel sword - to make up for this. In principle, the steel sword and steel mace should have roughly equal overall damage output, with the sword hitting more often for less damage per hit and the mace hitting harder, but slower.)
When armor and perks get involved, it can go either way, since the sword gains a crit chance while the mace gets to ignore a percentage of the target's armor. In general, with perks, the sword will shine against unarmored targets, while the mace will do better against those in heavy armor.