Sportscaster is a derived term from sports broadcaster. The definition of who is or is not a sportscaster is a broad one. The woman giving local sports scores on the evening news probably is not. Those who are play-by-playmen or analysts for the Big Three networks usually are.
Examples of sportscasters include Dick Vitale (college basketball), Jon Miller (baseball), and Howard Cossell (football, baseball, boxing, etc).
This term and this group of people are symbols of sports teams gaining more of a national audience in the US over time as home town sports announcers become bland and interchangeable. Compare the above list with names such as Harry Caray, who made his name as a local baseball announcer for the Cubs and the Cardinals.