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.
Best Answer
Yes, both effects can apply to the same spell.
There's nothing in the wording of either feature to indicate that it excludes other features adding damage as well. Many other combinations of features can work this way -- a barbarian's damage bonus from Rage is cumulative with their Strength damage bonus and other bonuses such as the Dueling fighting style. The word all of these have in common is add.
Contrast this with Thirsting Blade, which says:
It doesn't say "you can attack one additional time", so the reason it doesn't stack with Extra Attacks is that neither one adds attacks, they both just change the number of attacks from one to two.
This is also similar to how the barbarian and monk Unarmored Defense features don't "stack" with armor. Armor provides one way of calculating AC, Unarmored Defense provides another. A given character can only use one.
So, in general, effects or features that let you add something to a roll are cumulative, but effects or features that change a value are not.