The simple answer to your stated question is "Yes," though if you get into the details, nothing is really so simple.
All FM receivers start with something called the "front end." The function of the "front end" is to narrow the segment of the spectrum that is fed into the next stage, which is a series of superheterodyne stages the function of which is to convert the frequency of interest into the single frequency that your receiver is truly capable of decoding (which is usually 455 KHz).
The "front end" consists of a series of wide-band amplifiers and pass-band filters. Obviously, in order to have a wide range of capability, either (a) you have to have a front-end whose band-pass is so wide and so shallow as to provide zip selectivity (a common problem with inexpensive radios) or (b) you have to have a bunch of different front ends, which are switched into or out of the circuit depending on the selected frequency of interest.
An ICOM R7000, for instance, four separate front ends, each of which contains some pretty sophisticated BPFs that are themselves somewhat tunable. The result is pretty good sensitivity and selectivity while preserving a decent bandwidth. The downside is that the radio occupies more than a cubic foot of space, weighs more than 20 pounds, and costs a lot of money.