Just to be clear, FDNY and NYPD are two different systems, with different features.
In both systems, the mobile units transmit on one frequency (called "talk-in") and receive on another ("talk-out"). The dispatcher transmits on the talk-out frequency and receives the mobile audio from receivers on the talk-in frequency. The base station also re-broadcasts the mobile units on talk-out so other mobiles can hear them (but see below for a special difference with FDNY).
This is similar to a repeater, but there are some differences. First, the dispatcher is directly wired in to the base transmitter, and so never has to transmit on the talk-in frequency as they would if it were a simple repeater (the dispatch audio is just patched directly in on talk-out). Secondly, there's not just one receiver, but an entire network of them spread around the coverage area. The receivers are also called "voters"; their signals are sent to a central "comparator" that picks the receiver getting the strongest signal for rebroadcast by the base on talk-out.
Both FDNY and NYPD have some special features not found in many other systems.
For FDNY, the main feature is that the mobile re-transmission on talk-out is not automatic. The dispatcher has to switch it on manually after a mobile calls the dispatcher and off again when the exchange is finished. FDNY refers to the manual mobile retransmission mode as the "mixer", which I believe is terminology unique to FDNY. I'm not aware of many other departments that have the manual mixer feature; in most systems (including NYPD), the retransmission is automatic, as with a standard repeater.
The NYPD system is huge, perhaps the largest scale police system in the country. Some of the citywide channels have close to 200 voter receivers spread around the city, and even a local "zone" dispatch channel serving a few precincts may have 10 or 20 spread around the zone. They need this many receivers to provide good coverage in the urban geography of NYC, especially with portables inside buildings.
FDNY also has voters, but doesn't need as many as NYPD because of the way they use the system. Generally, NYPD offiicers portable radios to contact the dispatcher, while FDNY dispatch is primarily to higher power mobile units installed in the vehicles. (Individual firefiighter radios generally don't communicate with the dispatcher directly). Because of the higher power of the mobile transmitters, fewer voter receivers are required for good coverage.
A special feature you may not notice on the NYPD system mixes audio from the mobile units while the dispatcher is talking, allowing units to break in and be heard by all if they have an emergency. (In most systems, the dispatcher has priority over the mobile units).
Both systems are very impressive, given their scale and reliability.