I'm of the impression that "scrambled eggs" means the eggs are completely beaten to where the yolk and white are completely blended before being cooked.
And "over easy/medium/hard" is where the yolk is intended to be unbroken.
Assuming that's true, is there a specific term for when the yolk is intentionally broken, but not beaten/blended with the egg white, then cooked? So there ends up being distinct areas of white and yellow in the cooked result.
E.g. in the following picture, I cracked eggs right into a frying pan with a little bit of oil, then broke the yolks - and let them run where they wanted, flipping the eggs over once or twice to get it cooked all over - but did not try to blend or homogenize the yolk and egg white together.