It depends on who you ask. The common historical narrative is that Chan Buddhism developed out of a mixture of Nepalese Buddhism and Chinese Taoism. The idea being that the Buddhist monks visiting China from India were interpreted through a lens of Taoism. This then turned into Chan Buddhism, and was transmitted to Japan where it was then known as Zen Buddhism.
If you take this viewpoint, then you might say that Zen and what Siddhartha Gautama achieved were not the same thing.
However, most practitioners of Zen refute this and say that what Zen is, and what Siddhartha Gautama achieved are the same thing. This is the view that Wong Kiew Kit states in The Encyclopedia of Zen(referenced above).
People like Kit believe that Siddhartha Gautama discovered enlightenment on their own, and that enlightenment is the exact same kind of enlightenment as what modern Zen masters discover.
To quote myself now, "With only very rare exceptions, it requires an authority to transmit." It is not unheard of for students of Zen Buddhism to achieve enlightenment on their own.
Bankei, a famous 17th century Japanese Zen master, is recorded as having achieved enlightenment while watching a bloodied ball of phlegm slide down a paper wall. The story goes that he was so frustrated with the fake Zen masters in Japan at the time, that he sat on a mountain top until he first achieved tuberculosis and almost achieved starvation. Zen was so debased in Japan at the time that this was the only way for him to achieve it. All the other masters were fakes.
Among modern Zen masters it is understood that what Gautama Buddha achieved and what Bankei achieved are the exact same thing. That it was not transmitted to them is irrelevant, but it should be noted that this type of self-realization is extremely rare in Zen history.