If we wanted to add a nuance, the "gate" is the actual switching on of the receiver for the duration of observing the reflected signal (which can be as narrow as a single sample, which even a single sample for analog to digital conversions is an integrated observation over a sample time), while the range bin is which "gate" you are in. (Imagine a receiver that can have several gates covering the full possible range of the target). This originated from pulsed radar systems which is what my description above would apply to but can be shown to be equally applicable to other radar methods such as FMCW where an ambiguity in position can occur based on the repetition rate of the waveform.
For tracking, I believe this is where the term "Early-Late Gate" originated: In this use the gate is subdivided into an early half and late half (or can be described as separate gates, one slightly earlier and the other slightly later in vicinity of known target location), and the central portion of the gate position is adjusted earlier or later based on the difference between the early and late gate. Here too we are "gating" the received signal to limit our observation to a narrow time interval (or even one sample).