There's the National Highway System. (That all the roads and highways.) And there is the Interstate Highway System. (That's all the major highways that were funded in great part by the Federal Government, not by just the individual States.
There's superhighways in the Interstate system, but not all the highways are superhighways. To be honest, I haven't a clue where the dividing line is between what is a highway and what is a superhighway.
More Information on the US Interstate Highway System
Now, what do people say when they are about to head out on the highways?
They use the word "highway".
Only people discussing the funding or politics would use "highway system" in a conversation.
Joe(Americans like to shorten any term they come across)Nation