a judge: one who hears a case and pronounces a binding verdict or decision
At its core the word names the person who decides: the one with the authority to weigh a matter and hand down a verdict. It is the agent behind the common verb for judging (κρίνω means "to judge" or "to decide"), so a judge is simply "the one who does the judging."
The New Testament uses the word across a wide social range, but the underlying idea never changes. A local magistrate who tries a lawsuit is a judge; the leaders who ruled and rescued early Israel were its judges; and God, and then Christ, is the final Judge before whom everyone will stand. The word even stretches to describe people who set themselves up to pass sentence on others, which is why it can carry a sharp edge.
What shifts from verse to verse is not the meaning but the figure in view and the weight attached to the role. A courtroom official decides a case that can be appealed; the divine Judge decides a case that is final. Because English "judge" reaches across the same range, it renders the word cleanly wherever it appears.