Why is the American "Civil War" called that despite not actually being one?

By most dictionary/encyclopedia definitions I could find online, a civil war translates roughly to opposing groups vying for control of the same powerbase within the same borders, while what may be referred to as a war of independence or a war of secession/separation involves at least one party regionally breaking away (peacefully or otherwise) from a former union for self-government and facing centralist retaliation. (As far as I know, in the Confederacy's case, they officially fired the first shots on Fort Sumter, before the Union invaded them, but that's beside the point.)

The question is not asked from a place of trying to morally justify or neutralize the CSA's nefarious position in the particular context of the American division over slavery and its expansion etc. but rather with a concern of terminological correctness and curiosity on how much the CSA actually viewed itself as part of the same American nation or how much the Union pov held sway over political conceptualizations to warrant or rationalize this sort of phrasing that history just seems to accept at face value.

Does it really fit the bill for a civil war or internal conflict if we're talking about two distinct, self-declared nations, seated at remote capitals each, one breaking away from the other's jurisdiction albeit not trying to overthrow it per se?

By the same logic why don't we interpret the American Revolutionary War as a civil war between the 13 Colonies and the British government? (I'm not suggesting that we should, because the Revolutionaries weren't trying to overthrow the Monarch or the Parliament back home, but only to claim their autonomy therefrom.)

I notice the literature suffers a severe lack of nuanceful distinction between the legal, political, international implications of these two different terms which could use universal applicability without frequent reference to specific historical events.

some definitions of Civil War:

a war between opposing groups of citizens of the same country

https://www.merriam-webster.com/dictionary/civil%20war

a war fought by different groups of people living in the same country

https://dictionary.cambridge.org/dictionary/english/civil-war

a violent conflict between a state and one or more organized non-state actors in the state’s territory

https://www.britannica.com/topic/civil-war (Britannica seems to refute my position as the following paragraph includes secessionist insurgency in the definition)

some definitions of Secession or War of Independence:

formal withdrawal from an organization

https://www.merriam-webster.com/dictionary/secession

a war that is fought to gain independence

https://www.merriam-webster.com/dictionary/war%20of%20independence

the act of becoming independent and no longer part of a country, area, organization, etc.

https://dictionary.cambridge.org/dictionary/english/secession

The secession of a region or group from the country or larger group to which it belongs is the action of formally becoming separate.

https://www.collinsdictionary.com/dictionary/english/secession