BeiDou-3 navigation satellite system (BDS-3) has been fully completed and provides reliable positioning, navigation, and timing services to global users. To achieve compatibility and interoperability with other global navigation satellite systems (GNSS), B1C and B2a signals have been modulated by BDS-3 based on BDS-2, enabling frequency multiplexing with Galileo E1 and E5a signals. Inter-system biases (ISBs) are important for the fusion processing of different GNSS. This paper proposes an ISB estimation and application model based on single-differenced observations and analyzes the ISBs between the overlapping frequencies of BDS-3 and Galileo. Based on several receivers that can track the new BDS-3 signals, the characteristics of ISBs between BDS-3 and Galileo are revealed, and the real-time kinematic (RTK) positioning performance of BDS-3 and Galileo is analyzed. The results show that ISBs of B1C/E1 and B2a/E5a exist in different receiver types but not in receivers of the same type. Compared with BDS-3-only and Galileo-only solutions, the combined BDS-3 and Galileo solution improves both ambiguity resolution success rate and positioning accuracy by more than 10%.