EGOT.

slightly longish.
connect in no specific order:
actors John Gielgud, Helen Hayes, Audrey Hepburn, Rita Moreno, Whoopi Goldberg; composers Marvin Hamlisch, Richard Rodgers, and Jonathan Tunick; director / screenwriter Mel Brooks and director Mike Nichols.
Liza Minnelli, James Earl Jones and Barbra Streisand also fall in the above category but their accomplishment is slightly different from the rest. Explain the difference.