Eschatology (from the Greek ἔσχατος/eschatos, “[the] last”1) from the and the suffix -logy “the study of”), strictly speaking, refers to the formal study of the “End of the World”, both in its more classical theological context (hence its inclusion, for convenience's sake and nothing else, in the “theology” category) and its broader sense of any hypothetical event (or series of events) not necessarily confined to the purview of religion/mythology that could cause either major damage to humanity/reality as a whole (into which we include so-called “global catastrophic risks” and “existential risks”) or a change to it that is sufficiently drastic to permanently alter most or all known paradigms surrounding conditions of living.
It is generally accepted that the End of the World is inevitable but such inevitability is usually deemed too far into the future to be relevant. However, the presence of theories and threats that plausibly put this date into a much closer timeframe to the present time makes this a field of study worth considering.
Some theological authors opt to subdivide eschatology in general vs particular eschatology, where the former2) is dedicated to the study of events leading up to the End and the ultimate fate of Life, whereas the latter is concerned about the state of Man after death (while not being necessarily clear about whether this death happened before or after The End), more associated with things such as Final Judgments and so on, leaving the events leading to the End in the background. For the sake of clarity and orientation, “eschatology” here will refer to the former term.
“The End of the World” is a sufficiently ambiguous concept without a clear-cut defintion; while originally confined to the “end-times” proposed by most religions, because of its relatively recent overlap with a more thorough study on both past and hypothetically future catastrophes, scientific predictions of the far future, etc.3), the field's scope has broadened to the point that a strict conceptualization of the term remains rather elusive. At its core, however, it implies an event or series of events that at the very least cause the cessation of the component elements of “The World” (intended here to mean “reality”, in its totality or at least in its majority) as it is currently known and understood by humanity. This “End of the World as we know it” does not exclude the annihilation of reality and/or mankind, but it can also come to mean a drastic shift on life and its definition in all its spheres (“life” in itself, “life” in society, and so on) compared to what it was before the event in question - in a mysticist context, The End of the World is more of a final communion between earthly reality and the divine that the destruction of the universe as a necessary prerequisite.
With the advent of theories and ideas about the end of the world, usually (but not always) book-ended with the promise of a better (sometimes even eternal) life, some groups of people have decided to bring about the end of the status quo by themselves in a process known in contemporary theology as “immanentizing the eschaton”: that is to say, to actively bring about the end of the world to the material (i.e. “immanent”) world. Originally coined by Eric Voegelin in 1952 and popularized by William F. Buckley throughout the 60s and the 70s, the term originally meant to bring about, through political policies (in this case associated with Communism and Nazism alike), the actualization of the idea that disorder and injustice in the world can be corrected through unique insight and knowledge to the point of “bringing Heaven to Earth”.
Currently, it's meant not so much to mean the arrival of a new zeitgeist through political theory, but rather to encompass the actions of various individuals or groups to “hasten the end of the world [as we know it]”. While often associated with doomsday cults and contemporary religious groups, several non-theistic groups are also concerned with bringing about drastic changes to the modern world for the sake of establishing (what they believe to be) a better, usually utopical society. Thus, in this aspect immanentizing the eschaton is broadly speaking a form of accelerationism, an end-goal shared alike by transhumanists, terrorists, millenialists, and many others.
The term is also used by Discordianism in a much more different (or is it…?) context.
Trying to pin down End of the World scenarios into a category system is a rather difficult task as most properties that identify each possible apocalypse are actually shared by most. The closest thing to “categories” I can think of is discerning pairs of mutually-exclusive properties with which to define each brand of End Times. While trying to define these categories it became clear that, just like the definition of the “End of the World” per se, they're not as clear-cut as one could think of, as not only the definitions themselves but also their basis and criteria become increasingly subjective.
Soft vs. hard: This is defined by the final stage of the End of the World scenario in question. While a “soft” end of the world consists of a radical change of life, society, nature and reality, and with the continuation of these elements albeit completely changed from their former versions (an “End of the World as we know it” in which a new one -still mostly grounded in consistent conceptions of reality takes its place as a continuation), a “hard” end of the world implies the complete annihilation of mankind and/or the universe (depending how broadly one wants to measure the extent of the damaged caused by the scenario). A “soft” end of the world may have little to none human suffering, though it could technically also include great tribulations upon mankind that, while not eliminating it as a whole, could violently decimate it.
Mythological vs. Theoretical/Empirical: While one could call these two “Religious” vs. “Scientific”, I found it too much of a reductionist (though not necessarily incorrect) terminology. The former encompasses all End of the World scenarios as prophetized by narratives within a mythological entity - into which religious “End Times” prophecies are included as well4). Theoretical/Empirical are hypothesized predictions (a fancier synonym for “scientific prophecy”, anyway), infering from observation through a particular scientific framework and/or the observation and interpretation of evidence, respectively.
Natural vs. Artificial: This one, thankfully, it's much more easy to define - the End of the World will come about because of a naturally-occurring catastrophic event or by the result of action/inaction of living (and/or sentient) beings5). Whether these living beings are humans bringing about their own demise or something else entirely, from our planet or outside of it, well…
Terrestrial vs. Non-terrestrial: Perhaps the most self-explanatory one of the bunch. The End of the World has come from something on Earth or from something outside of it. Perhaps even both, who knows!
Immediate vs Mediate: This one is more concerned about the length of time in which the events that transpire during the End of the World take place: whether or not the End will come suddenly or instantaneously or if it's, after a “point of no return”, a drawn-out process. This could get muddy with some “early warning signs” of some prophecied apocalypses which may be interpreted as signs that the End of the World has already begun, although this category excludes them prima facie when not considered part of the phenomena characteristic of the irreversible stages of an End of the World scenario.
Known Date vs. Unknown Date: While it's the simplest category to grasp, perhaps it's the less clear-cut of them all when it comes to some examples. Some have dated the end of the world to a specific year and even a specific date and time, while others claim that they either don't know or can't know the date of the end times. Others (usually those describing possible catastrophes or cosmological events) give out a timeframe in which the event is likely to take place which kind of puts these scenarios neither in the “known” or “unknown” categories.
Past vs. Current vs. Near Future vs. Far Future: There are some who say that the End of the World has already taken place, while some says it is taking happening right now! If not, then that leaves any eventual End of the World into some point into the future - it could either be very soon!6) Or it could be so far into the future to be an essentially meaningless prediction, as some scenarios are dated several orders of magnitude of years later than the estimated lifespan of humanity/the solar system/etc.