What is the difference between a monologue and a soliloquy?

a. monologues have been used for centuries in theater; soliloquies are a relatively recent innovation.
b. monologues tend to be longer and more philosophical; soliloquies are more brief and emotional.
c. soliloquies usually involve more than one character; monologues involve a character alone onstage.
d. soliloquies involve a character talking to herself; monologues may be addressed to someone.