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The Space-Air-Ground Integrated Network (SAGIN) plays a pivotal role as a comprehensive foundational network communication infrastructure, presenting opportunities for highly efficient global data transmission. Nonetheless, given SAGIN's unique characteristics as a dynamically heterogeneous network, conventional network optimization methodologies encounter challenges in satisfying the stringent requirements for network latency and stability inherent to data transmission within this network environment. Therefore, this paper proposes the use of differentiated federated reinforcement learning (DFRL) to solve the traffic offloading problem in SAGIN, i.e., using multiple agents to generate differentiated traffic offloading policies. Considering the differentiated characteristics of each region of SAGIN, DFRL models the traffic offloading policy optimization process as the process of solving the Decentralized Partially Observable Markov Decision Process (DEC-POMDP) problem. The paper proposes a novel Differentiated Federated Soft Actor-Critic (DFSAC) algorithm to solve the problem. The DFSAC algorithm takes the network packet delay as the joint reward value and introduces the global trend model as the joint target action-value function of each agent to guide the update of each agent's policy. The simulation results demonstrate that the traffic offloading policy based on the DFSAC algorithm achieves better performance in terms of network throughput, packet loss rate, and packet delay compared to the traditional federated reinforcement learning approach and other baseline approaches.