Fan theories, much like fandoms, come in a wide variety. Here are some examples of the different kinds of theories:
In-Canon Theories: These fan theories usually try to explain plot holes, character origins, character motivations, and deeper lore within the story. These are the majority of fan theories where fans try to fix problems with their favorite works or try to add to it in order to gain even more enjoyment from it.
Speculations/Predictions: These fan theories usually use existing canon material and other evidence such as previews and trailers to form ideas of what will happen in an upcoming story line. These theories are very popular for major franchises such as Marvel and Star Wars before another installment is released.
Alternate Readings/Interpretations: These theories usually involve looking at piece of work through a different lens. Often times a creator does mean for their work to have more than one meaning and other times the audience will take away a personal interpretation. There is really no right or wrong when it comes to these theories.
Crossovers: Crossover theories are theories that will cross two or more franchises creating an unofficial shared universe. Some crossovers stem from an the same actor playing different characters, or easter eggs from creators paying homage to other franchises. Popular examples of this is the Tommy Westphall Universe that crosses over more than 420 tv shows into one shared universe and the Pixar Universe that crosses over all the Pixar animated movies into one shared universe.
Meta Theories: These theories are usually not about the events or characters within the canon but are instead about the behind the scene subjects. This could include relationship between actors/crew/writers, events that shaped the work and more. A popular example of this are the many meta theories surrounding Stanley Kubrick’s The Shining as seen the documentary Room 237.
Dream Theories: This is a common mechanism in some theories that places an entire story or parts of a story as being all a dream, hallucination, flashback, retelling or even visions that occur in the final moments before death.
Head Canons: These are usually theories with no evidence behind them but they are accepted as canon by an individual or a group of fans. These are sometimes not considered theories at all due to lack of any evidence and can often be more fan fiction than speculation.
Joke Theories: These theories are exactly what they sound like and are created for the purpose of being funny and often point out humorous connections or observations.