Monologue – A lengthy speech by a single character given to other characters in the play, this should not be confused with a soliloquy
Soliloquy – This is used as a device to let an audience know what is going on through a character’s mind. The speech given by the character is what the character is thinking. A famous soliloquy would be Hamlet’s “To be or not to be”
Ad lib – This is short for the Latin word ad libitum meaning freely. Essentially, it is the same as improvising lines. Usually used when lines are forgotten.
Exposition – The part of a play that fills in the audience on things that have already happened so they can make sense of who’s who and why they’re doing whatever. This can be done with the use of actual narrators who address the audience directly. Another way is to use the opening dialogue and have the exposition cleverly bound to it.
Deus Ex Machina – The Latin phrase means, literally, “a god from the machine.” It refers to the use of artificial means to resolve the plot of a play.
I like these definitions a lot. To add to your definition of soliloquy, putting that the actor is speaking directly to the audience (thus breaking the fourth wall) is significant. It also makes the other characters oblivious to the soliloquy.