Nihilism, in the sense of not believing in God, any purpose of life, any absolute truth, or life after death; is a subset of Atheism: all Nihilists are atheists; but not all Atheists are necessarily Nihilists.
For example, the Buddha and Lao Tsu, were atheist, but believed in Absolute Truth i.e., they were Mystics
I was atheist at an realty age. Became nihilist in college reading Shakespeare, Camus, and Neitzsche. Subsequently, I became convinced that Absolute Truth not only existed, but is the core of everyone's identity and all religion, as understood and mystically experienced by the founders of all religions