A roadway is any strip of road to which anyone can travel a certain distance to a destination with many other connecting roadways. Streets can be considered roadways since they are strips of road that connect and help you drive to a destination.
A highway on the other hand is a main, large, direct public road that is usually used within cities for entering and exiting. They have extra lanes (roadways have only one strip going forward, and one going back, while highways can have up to 4 separate lanes going one way, and vice versa).