Differential privacy, a vital concept in data privacy protection, has seen various paradigms emerge, ranging from centralized to localized approaches. This research explores two intermediate models known as the shuffle and pan-private models. These models bridge the gap between central curation and local user-centric data randomization, each offering a distinct balance between privacy and statistical utility. We delve into the necessity for different trust levels in these models, considering both engineering and mathematical viewpoints. In addition, we present a comparative analysis of the two models to clarify their differences.