Edge caching has emerged as an effective solution to reduce task processing latency in Multi-Access Edge Computing (MEC) systems by proactively storing potentially executable tasks on edge servers. However, most existing studies are based on the assumption of task homogeneity and fail to adequately consider the heterogeneity of task types in MEC systems. In real-world scenarios, computation-intensive and access-intensive tasks generated by users differ significantly in their processing procedures and resource demands. The previously adopted single caching and offloading strategy falls short in addressing the distinct performance requirements of both task types, resulting in inefficient utilization of computing and caching resources and a notable increase in system latency. To address this issue, this paper proposes a Task Pattern Classification-based Caching and Offloading strategy (TPCO). TPCO builds a unified framework to jointly handle both computation-intensive and access-intensive tasks, and designs two task-specific caching strategies: Gated Deep Q-Network (GDQN) for computation-intensive tasks and Neural Collaborative Filtering-based Caching (NCFC) for access-intensive tasks. Furthermore, a Bayesian optimization approach is employed at the global level to adaptively allocate storage resources between task types with the aim of minimizing system-wide delay. Simulation results show that the proposed TPCO framework outperforms existing methods under various conditions and reduces latency by at least 27.93% in heterogeneous task scenarios, offering a novel solution for joint caching and offloading optimization in MEC systems.