Aesthetic distance refers to the fact that the viewer (out of universe) and the character (in universe) do not necessarily know the same things. This works in both directions:
- The viewer knows who the killer is, but the protagonist cop does not.
- The protagonist cop knows his own past (e.g. a traumatic event), but the viewer is not yet made aware of this event that took place prior to the current story.
Dramatic irony refers to the fact that there can be a discrepancy between the (in-universe) objective truth and the (in-universe) character's belief about what is true.
Irony inherently requires a juxtaposition, i.e. (seemingly) contradictory things.
edit
Dramatic irony has more definitions than the one I just listed. But this definition is the only one that is relevant to my answer, so I'm omitting the others as they would only complicate the answer for no good reason.
An example:
An ex-convict, who we know is allied with the protagonist, is fighting an evil demon. The demon has taken the shape of a child. The ex-convict finally gets the upper hand and is close to defeating the demon.
Suddenly, a police officer walks by. What he sees is a bad guy (evil) attacking an innocent child (good), and the police officer points his gun at the ex-convict, because he tries to save the child. His notion of good and evil is reversed (juxtaposed) from the actual truth.
_____ is achieved when the audience is made aware of a disparity between the facts of a situation and the characters understanding of it
I think your interpretation of the question hinges on your interpretation of disparity. At face value, you are correct:
Disparity
A great difference.
A difference sounds semantically close to a distance, which would lead you to believe that the question is referring to aesthetic distance.
However, a juxtaposition is also a form of disparity. Disparity basically means "not being equal" (dis-parity = "non-equality", loosely speaking). Logically speaking, completely contradictory elements are also vastly different from one another.
Looking only at the word "disparity" could lead you to consider both aesthetic distance and dramatic irony as valid options.
But you should also focus on the rest of the question:
a disparity between the facts of a situation and the character's understanding of it
Aesthetic distance inherently refers to a difference between the viewer (out of universe) and the character (in universe).
But the question is focusing on two things that are both in universe (the actual truth, and a character's belief).
Therefore, aesthetic distance cannot be a correct answer. But dramatic irony still fits the bill, since dramatic irony can focus on two in universe elements.