Correct.
Buffy was approached by Merrick on the steps of her school (with Angel witnessing her calling, her first slaying of Robert Berman and crying in the mirror). Merrick found her late (she had already been called).
Buffy was told not to tell anyone, lied to her parents about why she was out, Merrick shot himself to save her from Lothos (different from the film), burned down the gym (different from the film), got expelled from school, ran off with Pike to Las Vegas on his motorcycle (there's a comic with this story), was sent to an asylum briefly (though this is possibly alternate reality due to Dawn's inserted presence--another comic with this story), her parents divorced, Joyce and Buffy moved to Sunnydale, etc...
Joyce and Hank never knew about Buffy being the Slayer. Joyce didn't learn about it until Becoming, pt. 2 (and subsequently threw her out of the house).