As a Hexblade warlock , does a Finesse weapon use CHA as a damage modifier?

So the description of a Finesse weapon is that when you make and attack and damage roll , you use either Strenght or Dexterity . And it must be the same stat for both rolls. However , Hex Warrior says that as a warlock you can use your Charisma as an attack modifier. Now since the finesse weapon description states that both rolls must be the same , and Hex Warrior modifies it to Charisma , does that mean that the damage roll also uses Charisma modifier , since they have to be the same?