An examination of the etymology of the word monologue reveals that it is a speech by one person [Greek: monologos speaking alone].
Shakespeare makes use of the monologue to entertain in a departure from the seriousness of action and often as a pivotal point of development of character, motifs, and plot. For example, Mercutio's rambling monologue in Romeo and Juliet explicates some of the plot of this tragedy as it provides a view that moves toward deflating the grand action of Romeo and Juliet's romantic promises to one another by reminding the audience of a more somber view of humanity since dreams are the "children of an idle mind." It also illustrates the motif of inconstancy as Mercutio rambles from one idea to another and Romeo accuses him of "speak[ing] of nothing."
As another example, in As You Like It, the famous monologue of Jacques on the stages of man reveals, of course, his cynicism. But, it also has such imaginative power that it transcends the action of the play.
- dramatic monologue
In contrast to the monologue, a dramatic monologue is a poem in which an imaginary character speaks to a silent listener. This poem is in the form of a speech or narrative in which the speaker unconsciously reveals certain aspects of his or her character during the description of a situation or certain events. By drawing conclusions based upon the speaker's words, the reader can piece together the poem's setting, the circumstances that prompt the character to speak, and the motives of the speaker, as well as his actions.
One famous example of a dramatic monologue is "My Last Duchess" by Robert Browning. In this poem, the reader can detect several traits of the Duke of Ferrara, among them the superciliousness of the Duke, his displeasure with his "last duchess" and retributive jealousy against her, as well as his excessive pride in displaying his portrait by Fra Pandolf, and the painting and the sea horse cast in bronze by Claus of Innsbruck.
While both a monologue and a dramatic monologue are basically the same thing, the difference between the two lies on very simplistic ideas.
A monologue (according to the eNotes site)
refers to a speech by one person in a drama, a form of entertainment by a single speaker, or an extended part of the text of a play uttered by an actor.
A dramatic monologue (as defined by Merriam Webster) is
a literary work (as a poem) in which a speaker's character is revealed in a monologue usually addressed to a second person.
Both the monologue and the dramatic monologue are both soliloquies (not to confuse further). A soliloquy is talking to ones self.
Therefore, to distingusih between the two, a monologue is not necessarily intended for a listener, whereas a dramatic monologue is intended for a listener.