I did spend some time with this terminological problem when writing a paper which heavily featured the term autocracy almost two years ago, but all my notes from back then are on my office-PC…to which I don’t have access to until further notice. So, this has to go from memory.

The short answer is that none of the terms have just one single meaning, they are very dependent on context and definitions (of which there never is just a single one).

However, each term has a certain tradition in past writing and in scholarship.

At its core, the concept of dictatorship refers to any form of government which concentrates all political power in the hands of either a specific class, group, or individual. I *think* (I might be wrong) it was the German Nazi-thinker Carl Schmitt who suggested that the root of any dictatorship lies in the fact that transition to the dictatorial rule is rooted in abrogating the extant (constitutional) rule, most typically by invoking martial law—which then is maintained in perpetuity due to the “crisis” which "necessitated" the move, being ongoing. Since this practice is seen quite commonly in pushes towards dictatorial rule in the 20th century (with several examples of this easily to be found in the news articles of the past years) there certainly might be some truth to it.

I think notable here is that dictatorship does not necessarily refer to the rule of a single individual, but may encompass groups (e.g., political parties).

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Despotism may imply that the ruler’s power is fundamentally unrestrained (i.e., that no constitution or other institutions restrict his freedom of action); but, arguably, this holds true for the dictatorship (and the autocracy) as well. It also implies a single ruling entity, not a group or party.

The term despotism as we typically use it originates in the writing of the French thinkers around the time of the French Revolution. Montesquieu established it to conceptionally denote the political system of monarchy (as opposed to the republic) with a strong moral evaluation of said monarchy, implying the exploitation of the common populace. He also did differentiate this type of monarchic rule from the constitutional monarchy.

This negative evaluation is not without critique, since monarchic/despotic rule is not inevitably to the detriment of the people, therefore coining the concept of “enlightened despotism” to imply a “benevolent” form of despotic rule. Nevertheless, this approach to the term of despotism is essentially interchangeable with (non-constitutional) monarchy.

In sum, you might understand “despotism” as the form of government non-constitutional monarchies adhere to, but it is not restricted to just monarchies in the European sense, but also encompasses similar forms of (typically monocratic) government all over the world (compare, for example, Karl August Wittfogel's writings on Oriental Despotism in the book of the same name).

For this association with monarchic rule, it is tendentially used to denote pre-modern forms of government, as opposed to dictatorship, which is, for all intents and purposes, a parallel concept within modern political systems theory.

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Now, autocracy has gained some popularity in recent years, especially in the form of referring to authoritarian political leaders as autocrats (i.e., Putin) within mass media.

In the context of historical research, autocracy is mainly used to denote pre-modern Russian monarchy. (I did have several conversations on how this Russian autocracy is to be defined in abstract means with scholars of the discipline, but no one could actually offer me a conclusive answer, so…I feel like it doesn’t really mean much beyond being the Russian spin on absolutism under a different name.)

However, I’ve seen it used in political science as the counterpart to democracy to within a an ideal-typical binary axis-model. In this usage, autocracy does not refer to a form of government, but it describes the mode of decision-making within a political system: authoritarian, top-down, decision-making by the few versus decision-making by establishing a consensus between many. This also implies that even in the modern democracy there are sectors which rely heavily on autocratic modes of decision-making (the military chain-of-command being the most obvious example).

In scholarly writing, however, there's about as many definitions of autocracy as there are writers who use the word. (Personally, though, I think using it in the way described—as an ideal-typical opposite to consensual decision-making —is workable.)

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To conclude, these kinds of terms (forgive me for skipping over tyranny; I’d not be able to go beyond Wikipedia with that one) are not exclusive to each other, but they are more firmly established within certain historical contexts and within the discourse of specific scholarly disciplines (e.g., Russian historiography, contemporary political science), who then will prefer one over the other terms (and might even bother to give you a definition). Still, the inherent vagueness and the multiple established usages for each single term, and the fact that their meanings, generally, do overlap to some extent, easily leads to a lack of non-separation within popular discourse, such as the mass media.

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To summarize, as a rule-of-thumb these terms have the tendency to be used like this (although there's probably a billion exceptions):

despotism = pre-modern autocratic rule

dictatorship = modern autocratic rule

autocracy = rule dominated by an authoritarian mode of decision-making