They are very similar. As a native English speaker, I would personally go to a dictionary to find out what the subtle differences are. Often it is a matter of fashion and politics. Different words were used at different periods of history. A foreign leader might be called a "dictator" if the speaker is opposed to him, or merely as "authoritarian" if the speaker accepts him. "Dictator" and "despot" emphasize that the ruler is an absolute ruler who rules by decree. "Tyrant" emphasizes the ruler as unjust and oppressive. There is a phrase "benevolent despot," a ruler with absolute power who uses it in a good way. There cannot be such a thing as a "benevolent tyrant." Also the word "dictator" comes from ancient Latin, it became popular and widely used to describe Hitler and Mussolini in the 1930s. So if you say "dictator" I think of modern dictators, from 1930 on. If you say "tyrant," I think of older times.

The three are almost synonymous, relating to autocratic leaders with total power, which they have often obtained by force. Despot and tyrant suggest a more cruel and aggressive regime than dictatorship, and these words are more often used in respect of history rather than modern dictatorships.