This is what Rawlings actually calls a skull cap, which is what I have always referred to as a skull cap. What John Olerud wore at first base is a pre-flap batting helmet. And what John Bench is wearing is also a
batting helmet.
And no, PWL, Johnny never wore his catcher's gear while batting. Except for that batting helmet he wore while catching.
And Garry Templeton was the last player I saw using the no-flap batting helmet, as he was grandfathered too. He also used it in the adult league he played in here.