It's essentially a TEPCO (or Jones, same design) translator.
Crystal controlled receiver, with local oscillator 10.7 above or below receive frequency, mixer circuit, and the 10.7 signal then amplified, as in a typical FM receiver. However, instead of detecting the FM signal, the 10.7 IF signal is then coupled into a crystal controlled transmitter, where the IF signal is mixed again with the local oscillator to derive the new signal on a different carrier frequency, then amplfied.
With a booster the receive and transmit frequencies are the same. The problem, of course, then becomes the contamination of the receive signal by the much stronger transmit signal. Hence the receiver is placed in a sheltered location, then using the intermediate 10.7 mhz frequency, sent by the long cable to the booster's transmitting amplifier. There it is beat against another crystal oscillator to upconvert from 10.7 to the operating frequency. As noted, there is much less attenuation at 10.7 mhz then at the FM band; and it is also easy to build traps at both ends to keep FM band signals from being couple from one unit to the other. Usually the cable is buried to prevent the shield from coupling booster signal back into the receiver.
As can be seen, whether it is a translator or booster, the characteristics of the off-air signal is preserved as it is "translated" first to 10.7, then to the new oeprating frequency. Where an off-air signal is demodulated, and the composit signal fed to a transmitter, the non-linearities of the demodulator and modulator change the signal. With this scheme, the only limiting factor is the IF strip. Too narrow, and some information (e.g. SCA) can be lost.
Using an STL and conventional transmitter for a booster (as we do now, is much simpler to engineer. We send the signal on a Moselely 606 composite STL to the tower where our sister FM is located, and use an MX-15 and Scala FMV for the booster.