Does a "frequency-modulated" signal mean that the frequency isn't consistent?

Does a "frequency-modulated" signal mean that the frequency isn't consistent? and therefore it has a specific bandwidth of frequencies is can cover??

• the change in PHASE is named BETA, computed as deltaF/Frequencyof Modulation. Thus if deltaF if 75,000Hz and the (music) tone causing that is only 150Hertz, the change in phase if 75,000 / 150 = 500 radians. Nov 2 '19 at 6:17
• Have a look at the MFSK section :) w1hkj.com/modes
– filo
Nov 2 '19 at 9:20

Frequency modulated means the instantaneous frequency of the signal is varied, with the instantaneous frequency carrying the information in the signal. This instantaneous frequency will only be of a limited range. If you provide more context we could help more.

therefore it has a specific bandwidth of frequencies is can cover

This is true of all signals. All signals have a specific bandwidth (aka range of frequency components that make up the signal via fourier transforms). Even amplitude modulated signals where the instantaneous frequency is constant (the carrier) have a bandwidth of frequency components that compose the signal.

A frequency modulated signal means that the frequency is shifted around a carrier frequency. This can be done digitally or via analog multiplication.

What it looks like is a sine wave speeding up or slowing down.

Yes, it normally has a specific bandwidth, some of the reasons being is radio licenses and bandwidth are in short supply (there are a limited number of frequency ranges). With frequeny modulation one can transmit more information in a given section of bandwidth. Most digital wireless communication uses frequency modulation.

Yes, it is a range of frequencies that are to be expected. In other words, frequency is a function of the modulated signal (or "input signal" if you want).