Crowd counting has drawn increasing attention across various fields. However, existing crowd counting tasks primarily focus on estimating the overall population, ignoring the behavioral and semantic information of different social groups within the crowd. In this paper, we aim to address a newly proposed research problem, namely fine-grained crowd counting, which involves identifying different categories of individuals and accurately counting them in static images. In order to fully leverage the categorical information in static crowd images, we propose a two-tier salient feature propagation module designed to sequentially extract semantic information from both the crowd and its surrounding environment. Additionally, we introduce a category difference loss to refine the feature representation by highlighting the differences between various crowd categories. Moreover, our proposed framework can adapt to a novel problem setup called few-example fine-grained crowd counting. This setup, unlike the original fine-grained crowd counting, requires only a few exemplar point annotations instead of dense annotations from predefined categories, making it applicable in a wider range of scenarios. The baseline model for this task can be established by substituting the loss function in our proposed model with a novel hybrid loss function that integrates point-oriented cross-entropy loss and category contrastive loss. Through comprehensive experiments, we present results in both the formulation and application of fine-grained crowd counting.