Having trouble knowing when to use "Capitol" vs. "capital"? Don't worry — you're not alone, and it's easy to mix them up (and you can mostly blame ancient Romans)! A quick explainer:

"Capital" comes from the Latin word caput, "head." It has an A because Latin usually forms adjectives from nouns by adding –al to their root ("finger," digitus –> digitAlis –> digital; "hand," manus –> manuAlis –> manual; "chest," pectus –> pectorAlis –> pectoral).

CapitAl means "related to the head" and so "the most important part of something." A capital city is the "head" city of a territory, capital punishment ends the functioning of a person's head, i.e. life (contrast corporal punishment, which harms the corpus, "body"), etc

This metaphor extends to architecture, where the "head" (top) of a column is called its capital, as well as finance, where capital is the "head" (most important component) of someone's assets (a folk etymology links "heads" of cattle to financial capital, but that's nonsense)

Side note: a head count is an example of a a figure of speech called "synecdoche," where you use a part of something to stand in for the whole thing (except under unusual circumstances, counting the heads in a group will give you the same number as counting the whole individuals)

CapitOl refers to a specific building, generally the United States Capitol building in Washington, DC, though other buildings that mirror the basic function of the U.S. Capitol locally, e.g. at the state level, also use the the word for their main governing/legislative building

The CapitOl is named after another, older space/building, the Capitolium in ancient Rome, which Romans saw not as their main governmental space but as the spatial embodiment of the State's most imp. protective deity, Jupiter Optimus Maximus (aka Super Duper Jupiter, Autobot Jove)

To make everything as confusing as possible, Romans retconned the etymology of the Capitolium to tie it to caput, "head," claiming as the temple's foundation was being dug, a preserved human head was found & seen as an omen that this would be the caput mundi, "head of the world"

Previous image is *not* the omen head, but the statue of Constantine in the Capitoline Museums, the most famous head in this space today (everyone's obligated to get a photo holding their finger up in front of it, I don't make the rules)

Eventually, Capitolium gets used for the entire Capitoline Hill, incl. the northeastern Arx (Citadel) where the Temple of Juno stands and the Asylum, a sacred grove in the middle where refugees to Rome were welcomed, though strictly speaking it's the area on the southwestern peak

As I said, the Capitolium contains the Temple of Jupiter, the site of Rome's poliadic cult (the worship of the city's/State's head guardian god — basically what Athena is to Athens), and so it's an embodiment of Rome's very power, sense of self-determination, and inviolability

The reasons are more complex, but that's essentially what stands behind the U.S. Capitol being named for the Roman Capitolium — it is the space from which U.S. power and governance is seen to emanate and the physical, architectural incarnation of the country's sacrosanctity.

So to sum up: Capitol = a specific and unique governmental building, capital = the top/most important example out of multiple instances of a class of things (also h/t to @jongraywb and @Heyyy_Kass for inspiring this thread!)