What is the Difference?
Capital, with an "a", refers to a city that serves as the seat of a government. Ironically, it is not capitalized.
Capitol, with an "o", refers to a building that houses a legislature. Like the names of other specific buildings, e.g., the White House, the Capitol is capitalized.
East, South, and North Capitol Streets are named after the building, so they are spelled with an "o".
The Capital Beltway is named after the city, so it is spelled with an "a".
There is no West Capitol Street. In its place, you will find the Mall, which, like other streets, is capitalized.
Like East Capitol Street, Capitol Hill is named after the building, so it takes an "o".
Inspired by HistoryProfessor.org.