Brillouin optical time-domain reflectometry (BOTDR) is a key technique for distributed fiber sensing of strain and temperature, but performance is constrained by the inherently weak spontaneous Brillouin signal. Here, we propose and experimentally demonstrate a novel frequency- and time-division multiplexed BOTDR (FTDM-BOTDR) based on a frequency-stepped light source generated from a frequency-shifting loop. In contrast with existing multi-frequency BOTDR, Brillouin signals from all frequency channels are coherently detected with a single local oscillator (LO) light, maximizing LO power and thus the heterodyne gain for all channels simultaneously. Furthermore, the temporal interleaving of different pump frequencies avoids excessive Kerr nonlinearities. A theoretical model is developed to analyze the signal-to-noise ratio (SNR) in FTDM-BOTDR and illustrate how this single-LO configuration overcomes the SNR limit in conventional multi-frequency BOTDR systems. Using 13 frequency channels, the system achieves the Brillouin frequency shift (BFS) precision of 0.298 MHz at 10 km and a maximum sensing range of 70 km with a 40 ms acquisition time, representing a 3.3-fold precision improvement and a 30 km range extension compared to single-frequency BOTDR. This FTDM-BOTDR technique overcomes key performance bottlenecks of conventional BOTDR and provides a scalable pathway toward high-SNR, long-distance, and real-time distributed temperature or strain sensing.