You probably have heard of the concept of Omnipotence and its paradox in philosophical discussions. Today we will properly define what exactly is it within fiction, to make it easier for everyone when you debate about these comic book characters in the future. A few things to clarify before we begin:

1. Omnipotence is not about Invincibility. If you are Omnipotent, you can allow yourself to be beaten.
2. Omnipotence is not about Might. Being able to become something isn't equivalent to being something already.

Some useful sources that I've found when researching for this article: Superpower Wiki, TV Tropes, Reddit and VS Battles.

Types of Omnipotence

Type 0: Meta Omnipotence

Also Known As: Author Authority

Because this is a list on Omnipotence in fiction, I can only make a quick mention about Meta Omnipotence before we start the list proper. It includes the power to affect reality, and if our "reality" isn't really real, the reality above still. Even though some characters like Deadpool have explored this concept, it was never really possible and within the scope of fictional characters, so no one actually ever use this in any discussion.

All in all, this type of omnipotence does not exist, at most only an imaginary ideal.

Type 1: Absolute Omnipotence

Also Known As: Infinite Power, Power-over-Logic, All-Powerful

Possessing all of the infinite number of powers in existence and non-existence. Even if the request does not make any sense, you can do it.

Most often attribute other facts about the user, such as being "unsurpassed", "unchallenged" or "have no equal". We cannot attribute anything because since the user can do anything, he is perfectly capable in making someone else more powerful than himself. The mere attribute undermines the potential for the user to determine otherwise.

Hence, most people don't usually refer to this type when discussing about Omnipotence because it is meaningless to do so. The moment when logic breaking comes into play we can no longer attribute anything, and the term Omnipotence itself loses meaning.

Type 2: True Omnipotence

Also-Known-As: Omnipotence, Literal Omnipotence, All-Powerful

Possessing all of the finite number of powers in existence. As long as the request make sense, you can do it even if it is conceptually impossible.

Unlike Absolute Omnipotence, True Omnipotence does not need to be absolute in every way, but only requires the user to satisfy the basic, literal requirement of being Omnipotent: having all (Omni-) power (-potence). While limitless power refers to even powers that are conceptually impossible, all powers just means all the power that there is. For example, there is no such power as "a stupid genius" or "a squarish circle". The user is still truthfully Omnipotent, because the user is not incompetent of doing anything, it is just that the demand does not make sense. Logic isn't some a mechanism buried deep within the universe, but simply something humans arbitrarily conceptualise. Not being able to "break logic" sounds very much like an inability, but reality doesn't concerns what humans think.

Of course, this definition is not without its problems. The Omnipotence Paradox states that if a being can perform any action, then it should be able to create a task which this being is unable to perform. This begs the question: if there is such that as impossibility or an impossible feat. If yes, then true omnipotence does not exist. If no, then true omnipotence does not exist either, because impossibility itself is something cannot be achieved.

Type 3: Practical Omnipotence

Also Known As: Maximal-Powerful

Possessing all the finite number of logically-possible powers in existence.

This is the best kind of Omnipotence that we can logically imagine. Being the direct contrast to Literal Omnipotence, the ability to do all that make sense (Tier 2). This is the ability to do all that is actually possible, or in most cases, within certain physical constrains of reality. Going back to the question "Can God create a rock so heavy that even God himself cannot lift it?" Let's assume one can only possibly create a rock up to A kg, and can only possibly lift a rock up to B kg. Depending on the nature of reality, one of which has to be smaller than the other.

However, this form of Omnipotence is also difficult to define. If Person A is able to be a stronger than a cow, but Person B is able to be weaker than a cow. The Omnipotent would have to choose which power and either way, one of them would be able to do one thing that the Omnipotent couldn't. So is Person A, Person B, both or neither of them practically omnipotent?

Type 3.5: Questionable Omnipotence

This type of Omnipotence does not really exist, but is only here simply due to the lack of perfect knowledge from the readers' perspective. Because even in theory, no amount of evidence or feats enable us to know for certainty if one can actually do everything. There are countless amount of things that one should be able to do before deemed as even practically omnipotent, therefore some feats, such as reality warping, are benchmarks that enable us to estimate to some level of certainty.

Type 4: Almightiness

To solve the paradox of Omnipotence, some may consider the idea of Almightiness. The user need not be able to do everything that everyone can do (which can be contradictory), you just need to be way more powerful than everyone else, so much so that no one can compete with you.

Of course, this is not really a type of Omnipotence, because in a world with only worms, even I can be "Almighty" since I am "way more powerful" than all of the worms.

On the other hand this concept isn't without its problems because power isn't something that can be objectively compared and ranked on a linear scale. There is no real "most powerful" when more often than not, I can't do some things you can, and you can't do some other things that I can't.

Type 5: Nigh Omnipotence

So powerful that it might seem Omnipotent, but not actually so. It is almost synonymous with Reality Warping, although very often Nigh Omnipotence covers more aspects than that.

A Nigh-omnipotent may or may not be Almighty and vice versa, though usually the most powerful nigh-omnipotent is considered Almighty.

Type 6: Specialised Omnipotence

Also known as Limited Omnipotence. Includes False Omnipotence and Cyberpotence.

The character is omnipotent within a field or concept.

Of course, this usually doesn't apply to "I am Omnipotent in my dreams." or anything like that.

Type 7: Godhood

Just powerful enough to be a "god".

Conclusion

Traditionally, the most accepted definition and understanding of Omnipotence is the idea of Absolutism, where the user can break all paradoxes and logic itself. Now logic isn't some universal truth embedded deep within the universe, it is simply an understanding arbitrarily created by human intelligence. So "breaking logic" isn't impossible, it just renders the concept literally meaningless for us to talk about. After all, an Omnipotent can make itself not Omnipotent, or "Fluggle a snuffin". What now?

When people began to understand Absolute Omnipotence as a useless concept (rather than an impossible one), Omnipotence becomes "all power that is logically possible". This definition simply removes the "powers" that does not make sense, such as "Fluggle a snuffin" (both words do not have meaning). This does not mean that there's something the Omnipotent no longer can do, it just removes the nonsensical "powers" that, literally, does not exist. This is called "True" or "Literal" omnipotence because it still fits the idea of "all power" in every literal sense, and is also the "default" definition for most people today.

However, this definition is not without its own problem of unrestricted comprehension, most well-known illustration being the "Omnipotence paradox" itself. Can it make something that its maker (or any being) cannot lift? Both making something and lifting something are logically sound, but the mere potential of one limits the other. Not everything that is sound in the literal sense is possible in the practical sense. Hence the idea of "Practical Omnipotence".

Suppose you have a list of all the powers in existence. Powers that also constitutes more of other sub-powers are ranked above. For example, the top entry would probably be "Omnipotence" since it constitutes all the powers listed below. Practical Omnipotence would be defined as having all the powers on the list, as long as it does not limit any of the powers higher up on the list. This is in my opinion, the most realistic definition for now.