Again, if this is not done correctly then modulation will change the perceived pitch of the note. This means that how far the carrier is modulated is equal up and down in Hz rather than in semitones. This is sometimes referred to as 'modulating frequency rather than pitch'. If this is not done, then increasing modulation depth (the amplitude of the frequency variation) will change the perceived pitch of the note as well as changing timbre, which is usually considered undesirable if you are trying to stick to a musical scale. The output of the modulation oscillator must be symmetric - extending equally above and below zero. However, there are some further restrictions needed in order to get good-sounding FM synthesis: In both cases, you have a sound-producing (carrier) oscillator and a modulation oscillator (whether it is called LFO or not), and the sound-producing oscillator's frequency is increased or decreased according to the instantaneous value of the modulation oscillator's output.
Yes, 'an LFO applied to pitch' is the same basic structure as 'FM synthesis'.
