well the front bumper refers to older cars id say pre 80'sish because some 80s cars and still cars today mainly trucks tho have bumpers but our cars have front bumper covers and a bumper reinforcement bumper.....etc
so picture wise
Bumper style car
notice the bare bumper with nothing on it etc.....yes its part of the car but you take that off there is nothing protecting the car its structural etc....
bumper covers like i said above cover up the bumper or reinforcement bar in a stylistic way.
So to your question yes there is a difference and to be honest there are people who still dont know that there is a difference..