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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.

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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:

You can attack with your pact weapon twice, instead of once, whenever you take the Attack action on your turn.

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.

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Yes they do, the rule of thumb if the effect has the same name it doesn't stack. Also as always talk to the DM and see what you can come up with together, if you try out an idea and its clearly OP then you can roll back that rulling.

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    \$\begingroup\$ Is this rule still relevant in 5e? I feel like it doesn't tend to give names to bonuses, other than the proficiency bonus. \$\endgroup\$ – Tin Man Feb 21 '17 at 19:43
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RAW, this works because of the wording (which you clearly know); however, your question seems to touch on if it's appropriate Rules as Interpreted.

As Mike Mearls (lead designer of D&D 5e) has indicated, they wanted to emphasize GM's doing what they feel is right more than exactly what the rules say, more than before.

In light of this, questions of 'this works by definition, but does it work in my game?' are better asked to each GM you'd like to use it for. The answer will just as likely be no, because the spells a Wizard casts and spells a Sorcerer cast are cast in a very different way, either using magical formulae or with your internal 'battery'... and it may or not make sense to them that one could affect the other. It is clearly not intended to be stackable.

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    \$\begingroup\$ "It is clearly not intended to be stackable" - Based on what? \$\endgroup\$ – JBC Feb 21 '17 at 16:43
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    \$\begingroup\$ You're going to get a lot of downvotes if you can't source that claim to something. In this scenario, the player has multiclassed Sorc/Wiz to gain this ability. What's left out is the high level Sorc/Wiz features they will NOT get access to in order to gain this particular power. \$\endgroup\$ – Lino Frank Ciaralli Feb 21 '17 at 16:57
  • \$\begingroup\$ @JBC based on similar abilities (such as the Wizard's Empowered Evocation) that cannot be applied to cross-class spells and the fact that Sorcerer/Wizard spellcasting are described as being very different, despite their spell lists. \$\endgroup\$ – Ifusaso Feb 21 '17 at 18:54
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    \$\begingroup\$ They can be described as very different, but in this case that's really not relevant. Spells are spells and abilities that work on spells work on all spells unless there's specific wording to the contrary. Note that even though the spells may be described as such, the spells known by sorcerers and wizards overlap quite a bit. Spell slots are shared between all your classes (you can cast wizard spells with "sorcerer" spell slots and vice versa). Given all that, it's kind of silly to try and exclude specific spells from working with the ability when there's nothing written that says to do so. \$\endgroup\$ – JBC Feb 21 '17 at 19:02
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    \$\begingroup\$ If you're going to make a claim like this, please source it. If you have no sources, then the claim is just your opinion. \$\endgroup\$ – Gryphon May 18 '18 at 17:23

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