A monologue is when there's more than one party involved, like two people talking to each other, but essentially all the talking is done by one person. Imagine a parent scolding a child, and the child doesn't respond. Or a comedian performing alone on stage in front of an audience. There's only one person speaking... but to someone else.
A soliloquy also implies only one person talking... but it's mostly in cases where there's no other participant in the communication. Like when you're talking to yourself. So, there's only one person talking again, but not to any one else.
