Technically, the super-hero in the red outfit with the lightning bolt and the white cape is not SHAZAM. SHAZAM is the egyptian wizard who grants Billy Batson the ability to transform himself into Captain Marvel.
Part of the confusion regarding the name SHAZAM is that "SHAZAM" is a much more distinctive name than "Captain Marvel". Marvel Comics have had a number of characters of the name "Captain Marvel" and hold the current trademark on the name. Thus, "our" Captain Marvel comics are published under the title of SHAZAM.