Sadly the answer is no to both.
It's perhaps an understandable mistake. They did share a resemblance and both got started in the business around the same time.
Eve Arden, born Eunice Quedens (she supposedly chose her stage name after looking over a perfume counter and seeing the names "Evening in Paris" and "Elizabeth Arden"), has been hailed in retrospect as a queen of film noir - a genre that didn't command much respect at the time either.
Her most famous role, a scene-stealing supporting turn in the gritty classic "Mildred Pierce," earned her the only Oscar nod she ever got.
She and horror-film legend Vincent Price met on neutral territory - a Western comedy - for the only film they ever appeared in together. The two were supporting stars in the forgettable 1950 film "Curtain Call at Cactus Creek."
Arden was already past her film-noir era and in the midst of earning contemporary fame in the light radio comedy "Our Miss Brooks." That series would later be turned into a TV series and earn her two stars on the Hollywood Walk of Fame - one for radio and one for TV. She died in 1990, at the age of 82.
Price, on the other hand, hadn't yet found his niche at the time of their convergence. He only earned respect much later in his career, again for his work in a genre that wasn't that well thought of at the time.
After toiling away for more than a decade as a supporting man in historical dramas and even a comedy or two, Vincent Price finally found his calling as a horror-film leading man in the 1953 cult classic "House of Wax." It was in such films, and later spoofs of them, that he found his considerable fame. He died in 1993, also at age 82.
But both did get their careers started around the same time. Arden's first credited role was in the Oscar-nominated 1937 comedy "Stage Door," while Price's first role was in the 1938 romantic comedy "Service de Luxe."
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