It is foreseeable that the BeiDou navigation satellite system with global coverage (BDS-3) and the BeiDou navigation satellite regional system (BDS-2) will coexist in the next decade. Care should be taken to minimize the adverse impact of receiver-related biases, including inter-system biases (ISBs), differential code biases (DCB), and differential phase biases (DPB), on positioning, navigation, and timing provided by global navigation satellite systems (GNSS). We present a method that enables time-wise retrieval of between-receiver ISBs, DCB, and DPB from multi-frequency multi-GNSS observations. Estimates of receiver-related biases between BDS-3 and BDS-2 are determined using all five available frequencies in different receiver pairs. The tests show that code ISBs are significant on the two overlapping frequencies B1I and B2b/B2I for a baseline with non-identical receivers, that epoch-wise DCB estimates of the same type in BDS-3 and BDS-2 can differ noticeably, and that DPB of BDS-3 and BDS-2 can have significant short-term variations depending on receiver baselines and frequencies.