If you expect something, you think it’s going to happen. If you got up at 4 in the morning, you can expect to fall asleep earlier than usual tonight.
If you expect (or anticipate) something, you are fairly sure that it is coming, though you might not be totally certain. You might expect to graduate from a certificate program on time, barring unforeseen events that prevent you from going to class. If you say, simply, “I’m expecting,” people will assume you’re pregnant. Someone disappointed in you might shake his head and say, "I expected more from you."