When a character speaks a soliloquy in a play, the character is alone (or believes that they're alone). Being alone, the character has no reason to lie to anyone. Whoever is speaking invariably tells the truth, at least as far as they believe it to be correct.
What the character says is purely subjective, of course, even if they believe that what they're saying is objective. Nevertheless, what the audience hears the character say is the truth.
A monologue is spoken to other characters, in the presence of other characters, or to the audience. The distinguishing aspect of a monologue is that the character is aware that someone else is listening to what they say.
As aside can be a mini-soliloquy, spoken to oneself, or it can be a mini-monologue, spoken to or in the presence of other characters, or it can be spoken to the audience.
In the play Amadeus, written by Peter Shaffer and first performed at the Royal National Theatre in London in 1979, composer Antonio Salieri is the protagonist. "Protagonist" is an odd designation for a person who confesses to killing Wolfgang Amadeus Mozart. Nevertheless, Salieri is the protagonist—he wouldn't have it any other way—and God and Mozart are his co-antagonists.
During the play, Salieri often speaks directly to the audience in monologues of varying lengths. At times, he moves in and out of the action of the play. Occasionally, he comments in asides to the audience on the action of the play that occurs around him.
Salieri often reveals his inner thoughts to the audience, but only in a monologue or an aside, not in a soliloquy. Salieri has no soliloquies in the play. He speaks only to the audience or to other characters in the play.
When Salieri first speaks to the audience in the play, he invites them into his room and into his world: Vienna in November, 1823. Salieri has already decided what he eventually confides to the audience at the end of the play, when the play comes full circle, back to his room in November, 1823.
SALIERI. ...You see, I cannot accept this. I did not live on earth to be His joke for Eternity. I will be remembered! I will be remembered!—if not in fame, then infamy....
From the beginning of the play, Salieri also decided to kill himself in defiance of Mozart's glory as a composer and in defiance of God.
SALIERI. And now my last move. A false confession—short and convincing. ...For the rest of time whenever men say Mozart with love, they will say Salieri with loathing. I am going to be immortal after all! And He is powerless to prevent it!
Thinking back through the play, does Salieri tell the truth in his monologues to the audience? Does he filter or color what he says to the audience to make his story believable to them? Does he tell the story to make the audience believe what he wants them to believe, regardless of the truth of the matter?
Throughout the play, Salieri is brutally honest with the audience about himself and his motivations. Is this simply a ploy to draw the audience into Salieri's version of the truth?
As the narrator, Salieri decides which events of his life he wants to share with the audience—if any of those events actually occurred. He also decides how those events are revealed to the audience. Because of the monologue and aside form, he controls the intellectual and emotional context in which those events are presented to the audience. Like any good playwright, Salieri presents those events for the greatest possible impact. He structures them in the way that he believes will lead the audience most convincingly to the climax of the play.
SALIERI. Now I go to become a ghost myself. I will stand in the shadows when you come to this earth in your turn. And when you feel the dreadful bite of your failures—and hear the taunting of unachievable, uncaring God—I will whisper my name to you: "Salieri: Patron Saint of Mediocrities!"
Yes, Salieri edits the events of the play psychologically as he retells them. Quite simply, there's no other way for him to tell his story in the way he wants it to be perceived.