This paper delves into the intricate landscape of privacy notions, specifically honed in on the local setting. Central to our discussion is the juxtaposition of point-wise protection and average-case protection, offering a comparative analysis that highlights the strengths and trade-offs inherent to each approach. Beyond this, we delineate between context-aware and context-free notions, examining the implications of both in diverse application scenarios. The study further differentiates between the interactive and non-interactive models, illuminating the complexities and nuances each model introduces. By systematically navigating these core themes, our goal is to provide a cohesive framework that aids researchers and practitioners in discerning the most suitable privacy notions for their specific requirements in the local setting.