Section 1983 is the remedial machinery for enforcing the Fourteenth Amendment. An essential element of a §1983 claim for relief is that the defendant acted under color of state law. The Fourteenth Amendment due process and equal protection clauses, and the incorporated Bill of Rights, apply to state action, not private action. Color of law under §1983 and state action under the Fourteenth Amendment mean the same thing.
Although §1983 and the Fourteenth Amendment draw a dichotomy between state action and private action, the real world is much messier than that. Private parties are often involved with government, and public officials have private lives, and it is not always clear whether was operated in one sphere or the other.