Previous works have investigated fundamental trade-offs in bistatic integrated sensing and communication (ISAC) systems, where the trade-offs are due to sharing the transmit resources between the sensing and communication signals. Interestingly, the ISAC trade-offs due to using an integrated multi-antenna receiver - where the communication and sensing signals cause interference to one another - are seldom studied. In this paper we study three bistatic ISAC structures, in which either the transmitter and/or the receiver serve as ISAC entities and study the transmit and receiverside trade-offs and the achievable sensing and communication performance. In the fully integrated scenario, both the transmitters of the sensing and communication signals and the receiver of the two signals are integrated, which serves as a benchmark for the cases in which either the transmitters or the receivers of the sensing and communication signals are separated. Specifically, we derive the classical and the Bayesian Cramé-Rao bounds, which indicate that relaxing the transmitter and/or receiver-side trade-offs benefits both the sensing and communications performance at the expense of using more hardware, antenna, and transmit power resources. These analytical and numerical results can serve as a foundation for designing the architecture for bistatic ISAC networks. Based on these insights, we discuss some open questions that require further research.