Like, if two players were roleplaying learning the casting of a spell, would it make any sense for the players in character to reference specifically the concepts of "verbal" or "somatic" in terms of the required components of a spellcast? 

My understanding is that these terms exist solely outside the in-game universe. Is my understanding wrong?

I'm sure the concepts must exist. They may have different in universe names/jargon but any spellcaster or instructor in spellcasting would know that spells require special sounds and movements.

Keep in mind, we don't as players speak common so we are already translating common into whatever language we play in (English at my table)

You're understanding is accurate enough. Terms like verbal, somatic, AC, and Hit Points are merely vocabulary abstracts that we (players & DMs) use to adjudicate the methods and results of something that happens in-game to the PCs.

The PCs will know specifically what the verbal and somatic components are, but they wouldn't know them by that term. They know that sounds and utterances with a specific pitch and resonance must be used, while making the required gesticulations with their appendages. Thet would also know that bat guano and pitch will also need to be at hand, or a diamond roughly the size of (insert carat count here).

I guess my follow up question how would you want to roleplay as an example a wizard instructing their apprentice? Are there terms you would prefer players use as the in world jargon?

Quote from Noksa >>

I guess my follow up question how would you want to roleplay as an example a wizard instructing their apprentice? Are there terms you would prefer players use as the in world jargon?

I imagine a wizard learning how to cast a spell as being instructed in incantation and (arcane) hand motions, or a cleric reciting a specific prayer and making a sign with the hand. It seems absolutely absurd to me for a character in world to turn to another character and say "the verbal and somatic components of this spell are as follows..."

Quote from socrlax24 >>

Quote from Noksa >>

I guess my follow up question how would you want to roleplay as an example a wizard instructing their apprentice? Are there terms you would prefer players use as the in world jargon?

I imagine a wizard learning how to cast a spell as being instructed in incantation and (arcane) hand motions, or a cleric reciting a specific prayer and making a sign with the hand. It seems absolutely absurd to me for a character in world to turn to another character and say "the verbal and somatic components of this spell are as follows..."

 I think we disagree on it being absurd, especially since it literally here's how you speak and move. They just feel like academic enough words to me that I could see someone with formal training use them.

If it bothers you that much try having a respectful conversation about why it bothers you and offer alternative words to you. If you would prefer you can just interpret it as jargon the character learned in a formal setting 

I see no reason why verbal and somatic spell components wouldn't be known by those names, honestly.  Especially to particularly academic spellcasters studying the arts arcane from a rigorous, mostly scientific viewpoint. When Anatomy of a Spell is a popular beginner's essay in your magical academy, you're free to assume that verbal and somatic components are well known. "The verbal component of the highly useful arcana generally known as 'Detect Magic' among the laity, though more properly known as Nyegram's Arcane Assensing amongst more finely educated scholars, is a particular incantation following the form of...", and so forth.

Self-educated hedge-witch sorcerers may not know those terms, but they'll be inventing their own terminology for everything and you can do as you like with them.  Or, frankly, with anything else. I like to marry Fluff and Crunch whenever I can, which is why I tend to refer to spells in character as being of the [X]th circle depending on their level, and spellcasters as being of the same circle as their highest reliable spells.  My tabaxi wizard, for example, is "an illusionist by initial training with a particular side penchant for transmutative arts, as the two often intertwine, and a mage of the seventh circle", rather than a 14th-level wizard. It's more fun that way, and it helps convey the idea that wizardly studies of magic are more structured, ordered, and scholastic than the all-day ass slappery that is sorcery.

Do you know what a conjugation is? A verb? Noun? Transitive verbs? Adjectives? Adverbs?

If the mechanics are there, the people will develop a system and associated vocabulary to help describe, communicate about it and learn how it works. The lesser educated might not be aware of the specific terminology, but just like we're aware of types if words that refer to names of things, types that are action words, describing words etc, they'll be aware that there's the spoken bit, the action bit and that material that you need to cast the spell. The more educated will have learned the terms for it.

Feel free to change the terminology to fit better with the culture, but the system would evolve.

If common is English, then yes.  If common is not English then yes but they'll call it something else. 

Why wouldn’t they? Technical people use technical terms. The layman’s whirly-gig is a mechanic’s flywheel because the mechanic knows the correct term. Why would learned scholars of magic refer to finger-wiggles rather than somatic components? 

There's no way they couldn't. They may not agree on what to call them, but what they call them isn't important.

Look at Fireball. "A bright streak flashes from your pointing finger to a point you choose within range and then blossoms with a low roar into an explosion of flame." It doesn't shoot from your elbow as you waggle it about like a chicken wing. It shoots from your pointed finger. That's the Somatic Component. Anyone who casts the spell KNOWS you have to point at what you want to be on fire.

You also can't say "MARGRET THATCHER SEXY 100%!" and have fireball work. You shout, "Fireball!" If you could, then my next wizard will be Courage the Cowardly Dog, and I'll just panic, "Obija obija obija!" For every spell.

I get that a lot of DM's give Subtle Spell the shaft by ignoring these components, but that's how these spells work every time until your DM says otherwise. They'll understand that there's a thing said and a thing done. Not all spells need you you to give someone the finger. Not all of them require you to shout. Not all of them require bat poop... but some do, and fireball needs all three, so anyone who can cast spells is aware of the concept. They just might not have the Greek required to call it Somatic.

We do not role play the verbal or somatic components of any spell.

But we do use the fact that a specific spell has those components for the role play. If your hands are bound you obviously can not use somatic components and the same for being gagged.

I think the last two comments got off topic. We are discussing the words to use in and out of character when characters are discussing how to cast a spell. No one is suggesting ignoring or not using somatic or verbal components.

The two responses I see are:

"there is no problem with characters saying somatic and verbal"(my opinion)

"characters would use different terminology in world" (my understanding of the op's opinion)

Edit: also want to note this is a playstyle conversation not a mechanics/rule conversation 

I'm of the mindset that things like "Somatic Component" and "Verbal Component" would be the correct in-universe nomenclature. Especially for a wizard, whose spellcasting is based on study and education, as opposed to classes like Bards whose magic is a combination of performance and force of will. I think some terms don't make sense as things to say out loud... what would HP be? How do you define AC as a concept?

But a spell with a somatic component does literally require the movement of at least one hand in order to cast. An individual spellcaster might not have their own term for that, but any academic who records such details would need an accepted common term to apply when discussing spellcasting. Unless the DM wants to take the time to come up with their own common term within their setting. Somatic Component seems like the logical thing for someone who's well educated to use when discussing spells that require hand motions to cast.

You could call them different things in different schools. Mantras and mudras, for example. Chants and gestures. Etc.

The words "somatic" and "verbal" weren't invented by Gary Gygax or WOTC. They're concepts that exist outside of D&D. It's like asking if, in-game, a curved steel slashy thing would be called a "scimitar". Why wouldn't that word be used? That's what the thing is.