A 6th level Draconic Bloodline Sorcerer gets the Elemental Affinity feature, which states:
...when you Cast a Spell that deals damage of the type associated with your draconic ancestry, you can add your Charisma modifier to one damage roll of that spell.
A 10th level School of Evocation Wizards gets the Empowered Evocation feature, which states:
Beginning at 10th level, you can add your Intelligence modifier to one damage roll of any wizard Evocation spell you cast.
Even though the Elemental Affinity is a result of a sorcerer class feature, it doesn't actually say that damage needs to be from a sorcerer spell, or from any magical origin at all, so it could apply if the caster caused the damage with a wizard spell.
If a Wizard 10/Sorcerer 6 character with the appropriate school and ancestry were to cast an evocation spell they have prepared as a wizard, would they apply both their intelligence modifier and their charisma modifier to the one damage roll, assuming the damage type matched that of their draconic ancestry? For example, if this character had Red Dragon ancestry and cast Fireball, would the damage be 8d6 + Int + Cha, or would they have to choose between applying their Int modifier or their Cha modifier?
I'm a bit confused since even though these features have different names, they have very similar effects (applying an ability modifier to damage), in the same way that a Warlock's Thirsting Blade invocation is similar to the Extra Attack feature but those two features do not stack.