The example I am thinking of is the difference between the Spartan Kings and the tyrants of other city states, but explanation of any other example is welcome.
The word τύραννος and its derived terms were, in the Archaic Period, used more or less synonymously with other words for kingship, although it seems to be a label applied by others, not the king himself. In Archaic Greek a king was generally called a tyrant rather than any other type of king when the rest of the aristocracy found him arrogant or excessively ostentatious with his wealth. But by the Classical Period in Athens the term tyrant had become associated particularly with a more oppressive form of autocracy, which barred not only the aristocracy but also the people from even advisory roles--this is usually how Herodotus uses it, and it is metaphorically extended to the democracy in some Athenian texts. But the most mature definition of tyranny was Aristotle's, which carried in modified form to the Roman Period. Aristotle defined tyranny as essentially the "bad" form of monarchy, but not strictly in a moral sense. Rather Aristotle defined tyranny as unlawful monarchy, monarchy in which the king had no legitimate claim (e.g. Pisistratus), was not readily accepted or was imposed by force, or was consciously harmful to the people. The Roman conception was similar--whereas the quintessential tyrants for the Athenians were the Pisistratids and the Great King, the Romans looked back on the Tarquins, whose injustice earned them the label in later writings of tyrannus