[Boogieman]

“The Romans used it to describe both wars that were waged to overthrow the government entirely, or to alienate territory from the government.”

The second category doesn’t fit either. The South seceded peacefully and was governing itself, and then the war started after that, as a war between two sovereign nations.

[wideawake]

The second category doesn’t fit either. The South seceded peacefully

No it didn't.

Did the Union fire on itself at Fort Sumter?

Was Edmund Ruffin a deep cover Union plant who carried out a false flag operation?

[BroJoeK]

Boogieman: "The second category doesn’t fit either.
The South seceded peacefully and was governing itself, and then the war started after that, as a war between two sovereign nations."

But "the South" did not secede peacefully!
It was unlawful and violent from Day One, December 1860 -- seizing dozens of major Federal properties, threatening Union officials, firing on US ships.
There was nothing "peaceful" about it.

Then in April, 1861, the Confederacy started Civil War by launching a long-planned military assault on Union troops in Union Fort Sumter, and on May 6, 1861 formally declared war on the United States, at the same time sending military aid to pro-Confederate forces in the Union state of Missouri.

Here is a definition of "civil war" which certainly includes the US from 1861 - 1865:

A civil war is a war between organized groups within the same state or country,[1] or, less commonly, between two countries created from a formerly united state.[2]
The aim of one side may be to take control of the country or a region, to achieve independence for a region or to change government policies.[1]

Neither the United States nor any major power on Earth ever recognized the Confederacy as a legitimate independent country.