The stage was different, and so was the tone. But the voice was unmistakable.

Fran Drescher, the owner of a distinctly nasal, Queens-inflected accent, made her name in Hollywood for her starring role in the sitcom “The Nanny.” On Thursday, she appeared before dozens of cameras as the president of the actors’ union that voted unanimously earlier in the day to go on strike, delivering a fiery argument depicting the stakes of the decision.

“The eyes of the world and particularly the eyes of labor are upon us,” Ms. Drescher said. “What happens to us is important. What’s happening to us is happening across all fields of labor.”

She shook her fists in indignation. “I am shocked by the way the people that we have been in business with are treating us!” she continued. “It is disgusting. Shame on them!”

Ms. Drescher is the latest in a long line of familiar faces — Ronald Reagan, Patty Duke and Charlton Heston among them — to run SAG-AFTRA, the union that represents…