I'm not certain the distinction is as clear-cut as you're making it sound. "King" was certainly a standard insult in 19th-century US politics for a president seen to be overstepping his authority (like Abraham Lincoln or Andrew Jackson). And "lord" is still a negative word in English when used as a verb.

Mainly, the distinction between the King and the Tyrant comes from the Greek.

The first use of the word turannos (tyrant) is found in the works of a poet, Archilocus of Paros. In a segment on Gyges, the legendary rich king of Lydia, he writes :

I do not care about the possessions of Gyges rich in gold. Envy has not yet taken hold of me. And I am not indignant about what the gods do. Nor do I lust after great tyranny. For it is far away from my eyes.

So at this time (c. 650BC), you already have an association between wealth/greed and tyranny.

There is already quite a negative association (greed, lust for power) but very different from the autocratic meaning we have today.

Theognis of Megara (c. 550BC) encourages people to rebel against the tyrant figure (Elegy 1180-1182) which he calls "demophagos" = devourer of the people. The image of the "hungry" tyrant was used by other authors.

but a despot that devoureth the people, to lay him low by what means soever it please thee, is no cause for wrath from Heaven.

More generally, the sources distinguish well the King (Basileus) and the Tyrant (Turannos). The former refers to a power sanctionned by the law (be it hereditary) while the latter is viewed as unjust.

In Plato's Republic (Book I), Thrasymachus calls tyranny "the extreme of injustice and wrongdoing":

Tyranny is not a matter of minor theft and violence, but of wholesale plunder, sacred and profane, private or public.

Finally, the opposition seems to be formalized by Aristotle in his Politics:

The deviation from monarchy is tyranny; for both are forms of one-man rule, but there is the greatest difference between them; the tyrant looks to his own advantage, the King to that of his subjects.

So in the end, you have this double opposition: public interest vs self interest ; sanctionned by law vs unlawful.

Starting with 'despot'. Aristoteles and Plato defined the different types of government by how many people there were in power, and by the character of righteousness: Monarchy (one person), Aristocracy (few), and The Republic (many). These were the righteous ones, those with fair and legitimate laws. The unlawful counterparts to thes e were called Despotism, Oligarchy, and - surprisingly - Democracy. As Aristoteles and Plato were extremely influential, the words they used obviously had a huge impact on the language. One may wonder then, why 'democracy' has not retained it's negative connotation. It should be noted that during Aristoteles' time, slaves and common people were considered to be fundamentally less fit to rule, and therefore they considered a government were everyone had power to be inherently bad.

Now, the term dictator comes from ancient Rome (the republic), where the power was split between two consuls. The two of them being of equal power naturally meant, that effectiveness was somewhat sacrificed. In times of emergency however, a dictator would be elected, to act swiftly and undisputed, to save the republic. An example of this is during The Second Punic War, were Quintus Fabius Maximus were elected dictator, in order to deal with Hannibal, who had run rampant in northern Italy for years. He, despite extreme unpopularity and protests from the Romans, refused to meet Hannibal in open battle, instead resorting to raiding and irritating his foe (now called Fabian Strategy). This eventually exhausted Hannibal's army, winning the war for Rome. After the war, Fabius stepped down, and all was back to normal. This was the intended use of a dictator. However, starting with Cornelius Sulla, the dictatorship was later abused, with generals seizing power and raising themselves to dictators for life, most famously by Julius Caesar. Thus, the title of dictator had become soiled.