The new concept of semi-integrated-sensing-and-communication (Semi-ISaC) is proposed for next-generation cellular networks. We propose a novel Semi-ISaC framework which provides more freedom as it allows that a portion of the bandwidth is exclusively used for either wireless communication or for radar detection, while the rest is for ISaC transmission. To enhance the bandwidth efficiency (BE), we investigate the evolution of Semi-ISaC networks from orthogonal multiple access (OMA) to non-orthogonal multiple access (NOMA). First, we evaluate the performance of an OMA-based Semi-ISaC network. As for the communication signals, we investigate both the outage probability (OP) and the ergodic rate. As for the radar echoes, we characterize the ergodic radar estimation information rate (REIR). Based on these metrics, we derive the analytical and asymptotic expressions of the ergodic RIER. Then, we investigate the performance of a NOMA-based Semi-ISaC network. More specifically, we derive the analytical expressions of both the OP and of the ergodic rate for the communication signals. The asymptotic expressions of OP are also derived for quantifying the diversity gains of the communication signals. As for the radar echoes, we derive the analytical and asymptotic ergodic REIR. The high signal-to-noise ratio (SNR) slopes are also evaluated. The analytical results indicate that: 1) Under a two-user NOMA Semi-ISaC scenario, the diversity order of the near-user equals to the coefficient of the Nakagami-m fading channels ($m$), while that of the far-user is zero; and 2) The high-SNR slope for the ergodic REIR is based on the ratio of the radar signal's duty cycle and the pulse duration. Our simulation results show that: 1) Semi-ISaC has better channel capacity than conventional ISaC; and 2) NOMA-based Semi-ISaC has better channel capacity than OMA-based Semi-ISaC.