Not to be confused for a Subject. For a comparison, read Subject Versus Theme.

This is the broadest yet most specific definition of a theme. And yes, ‘any’ means ‘any’.

Themes don’t necessarily have to be intentional, as themes can end up being emergent without the author intending it. Though this shouldn’t be confused with Death of the Author.
Though when people (amateur YouTube critics) talk about themes, they tend to not talk about the emergent ones but the ones that are intentionally placed in a film.

Examples of the type that are intentional would be Do Androids Dream of Electric Sheep? in Blade Runner and “Life, uh, finds a way” in Jurassic Park. Coincidentally, neither of those films explore those specific themes properly. Jurassic Park, in fact, has a different emergent theme: showing the consequences of Zoo mismanagement.

Death Note is probably the pre-eminent example of a work that has an emergent theme: as it sorta, kinda, not really explores the question of what justice is, embodied by Kira or L.
Emergent themes are usually a side-effect of good storytelling – though this is not something that should be relied upon as a guarantee and, further, the presence of an emergent theme isn’t necessarily an indicator of good storytelling.
An emergent theme is also a side-effect of bad storytelling, since a poorly-written plot might have a radically different theme from the intended theme.

Exploring the theme is not the same as mentioning it. Exploring involves raising the idea/question and then showing it play out in real time.

Using the example above of Jurassic Park’s Zoo Mismanagement theme: it shows the consequences of mismanagement, as well as the specific things that contribute to that mismanagement.
To give specifics (though not too many!) on those contributing factors: the entire computer system is managed by one guy, who isn’t paid enough; park employees don’t know enough about the animals they’re meant to take care of to actually take care of them; many of the enclosures are too small; they don’t realize they can sedate dangerous animals before moving them.
Now for consequences: the park’s computer system is hijacked, resulting in a blackout; animals become sick; animals start escaping the second they have the opportunity to; a man was eaten by Raptors; many people died.

In contrast, mentioning a theme generally means that you point at it and go “Do Androids Dream of Electric Sheep?” and then calling it a day. You don’t really show the specifics of what contributes to that theme, or show consequences…or really do anything.
Viewers can also mis-identify themes just by assuming that exploring is the same thing as mentioning.

This is focused around something very specific. Themes can often be screwed up by the original creators – as in the example of my apparent favorite punching bag: Jurassic Park. Themes can also be mis-identified by the audience (or critic), who sees something that was never intended.

A question that can be asked is…how do you determine the difference between these? And how can you tell if you’re just seeing things that aren’t there versus seeing something that is there that wasn’t intentional?

After thinking about this, I think I’ve come to a conclusion: it has to do with the Subject.
The themes of a story generally have to be connected to the subject of a story – to put this bluntly: what it is about in an abstract sense has to be related to what it is about literally.
If the theme isn’t directly connect-able to the subject…then there’s been a failure in actually communicating the theme.

This is also why, generally, stories can’t really explore complex specific modern themes (like, I dunno, the ills of cryptocurrency) in a Fantasy setting. It just doesn’t connect together. In contrast, much simpler general themes (the bond between a father and son, for example) can be explored in virtually any setting.

I almost forgot what I actually called this section. The other major aspect of determining whether a theme is in your head or not has to do with the context of the story.
Basically, some things in the story will either support or undermine the theme. In Jurassic Park, the theme Life, uh, finds a way is undermined by the park being badly designed. In contrast, the Zoo Mismanagement theme is supported by the park being badly designed.
A different example is the film The Platform, which I haven’t seen, but I have seen this video about it. The intended theme of that film is that capitalism is bad. However, that theme is undermined by two things:

1. The fact that you cannot meaningfully connect the theme to the subject.
2. The fact that the food is being granted to everyone through a centralized conveyor which literally goes top-down, which is not capitalist. Capitalism is explicitly decentralized.

The film actually is a better “socialism is bad” film than a “capitalism is bad” film (oops). Though in either case you still can’t meaningfully connect those themes to the subject of the film. More broadly, it can be interpreted as saying that “even if you did your best to share resources equally, there might still never be enough”.