"Besides" and "except" have virtually the same meaning, coming from a native speaker. The only difference between them is that "except" is slightly more formal in my opinion. "Besides" is usually used for everyday conversation. On the other hand, "to expect" has no relation to the other two words you asked about, it only sounds similar. Your definition is correct though:)

I think you want to know the difference between "besides" and "except" because "besides" and "expect" are completely different words. "Expect" means to believe that something will happen or somebody will do something.