I do accept that "Wizard Spells" are spells on the Wizard Spell List, while "your Wizard Spells" are specifically spells on the Wizard Spell List that are "yours." Wish is a Wizard Spell, but it is your Wizard Spell once you learn it/know it/prepare it. I do not concede that it is only your Wizard Spell if you learn it/know it/prepare it specifically as a result of a Wizard level. 

See #9 above, I do think that the line around what spells are "your" is a little fuzzy for spells granted outside of a normal slot-based spellcasting feature, and depending where it's drawn, could have some interesting results (like permitting a racial caster to cast their racial spells with spell slots, if they have a Spellcasting feature from a class for which those spells appear as Class Spells). 

Quote from Chicken_Champ>>

I do accept that "Wizard Spells" are spells on the Wizard Spell List, while "your Wizard Spells" are specifically spells on the Wizard Spell List that are "yours." Wish is a Wizard Spell, but it is your Wizard Spell once you learn it/know it/prepare it. I do not concede that it is only your Wizard Spell if you learn it/know it/prepare it specifically as a result of a Wizard level. 

See #9 above, I do think that the line around what spells are "your" is a little fuzzy for spells granted outside of a normal slot-based spellcasting feature, and depending where it's drawn, could have some interesting results (like permitting a racial caster to cast their racial spells with spell slots, if they have a Spellcasting feature from a class for which those spells appear as Class Spells). 

I think I could fall on either side of 'can you use your racial trait/feat spells with your class slots?' question, in terms of balance. Neither option seem out of scale with power, but spellcasting features certainly do only appear to give you the ability to cast a spell associated with a class, which is obviously a thing ("Each spell you know and prepare is associated with one of your classes, and you use the spellcasting ability of that class when you cast the spell.")

Quote from Chicken_Champ>>

I do accept that "Wizard Spells" are spells on the Wizard Spell List, while "your Wizard Spells" are specifically spells on the Wizard Spell List that are "yours." Wish is a Wizard Spell, but it is your Wizard Spell once you learn it/know it/prepare it.

Ok, but your argument hinged on "wizard spell" having exactly one meaning. You can't prove your interpretation is correct based on how the phrase is used in one place if it's also used differently elsewhere.

I do not concede that it is only your Wizard Spell if you learn it/know it/prepare it specifically as a result of a Wizard level. 

I think the rules disagree with you on this one.

The Wizard table shows how many spell slots you have to cast your wizard spells of 1st level and higher. To cast one of these spells, you must expend a slot of the spell’s level or higher. 

If casting your wizard spells requires expending a spell slot, when a drow wizard casts Darkness using their Drow Magic trait, they're not casting one of their wizard spells.

You prepare the list of wizard spells that are available for you to cast. To do so, choose a number of wizard spells from your spellbook equal to your Intelligence modifier + your wizard level (minimum of one spell). ... You can change your list of prepared spells when you finish a long rest.

If you didn't prepare the spell from your spellbook, it's not part of the list of wizard spells available for you to cast.

Intelligence is your spellcasting ability for your wizard spells, since you learn your spells through dedicated study and memorization.

If a drow casts Darkness or a sorcerer casts Wish using Charisma, how can it be one of their wizard spells? Your wizard spells are cast using intelligence.

It's clear your wizard spells, the ones you can cast, are the ones you prepared through the wizard's spellcasting feature. It's not unreasonable to interpret Overchannel's "when you cast a wizard spell" as "when you cast one of your wizard spells", even if it's not the only reasonable interpretation.

Also consider the Wizard's Cantrip Formulas from Tasha's Cauldron of Everything:

Whenever you finish a long rest...you can replace one wizard cantrip you know with another cantrip from the wizard spell list.

It's pretty obvious what they mean by "one wizard cantrip" here: it's a cantrip you learned through the wizard class. Insisting that you can replace one of your sorcerer cantrips because it happens to be on the wizard spell list is silly.

Speaking of which, it seems the designers are trying to avoid using two separate meanings for "[class] spell" going forward. They could've written "you can replace one wizard cantrip you know with another wizard cantrip" there but didn't.

EDIT: Forgot to bring up the optional rules for identifying spells in Xanathar's Guide:

If the character perceived the casting, the spell’s effect, or both, the character can make an Intelligence (Arcana) check with the reaction or action. ... If the spell is cast as a class spell and the character is a member of that class, the check is made with advantage. For example, if the spellcaster casts a spell as a cleric, another cleric has advantage on the check to identify the spell. Some spells aren’t associated with any class when they’re cast, such as when a monster uses its Innate Spellcasting trait.

I know this isn't part of the core rules, but it very clearly lines up with both the Sage Advice Compendium answer and the bits of the Spellcasting feature I quoted earlier.