A soliloquy is one variant of a monologue, which is a speech spoken by a single character. The soliloquy is spoken by the character alone on the stage, giving the impression of conveying an interior state, or sometimes in the presence of other characters but apparently not addressed to them.
Certain plays and characters, namely Hamlet, often match soliloquies with the character's personality. In King Lear, Shakespeare rarely does that.
Lear's "Blow, winds, and crack your cheeks!" monologue in Act III, Scene 2 is considered a soliloquy because he is not conversing with Fool. Rather, he is addressing the winds and other elements, and in many respects describing his interior state.
Here I stand, your slave—
A poor, infirm, weak, and despised old man.
Edmund's "Thou, nature" speech in Act I, Scene 2, with its concluding line, "Now, gods, stand up for bastards!" is another well known soliloquy.
While Goneril and Cordelia have monologues, those are not soliloquies.