To others:
Other ways to say these things are "modulator", "FM depth", and "carrier signal", respectively.
Also, you can have FM pads, e. pianos (EX: DX7, or maybe this), etc. and have them be warm even without post-processing. You'd just need to be very particular about the modulation depths and subtractive synthesis incorporation, even if it's all internal to the synth, so that it sounds swell out of the box. Mixing in a comb filter may actually help, too, if done carefully.