Is BCH tied to BTC?

Could you elaborate on whether BCH, or Bitcoin Cash, is somehow tethered to BTC, or Bitcoin? Is there a direct correlation or dependency between these two cryptocurrencies? Does the price movement of one automatically impact the other? Do they share any fundamental technological characteristics or do they operate independently? Additionally, how does the community and market perception of each cryptocurrency factor into their relationship, if any? Could you please clarify these points for me?