What is the difference between frequency modulation and phase modulation?
A signal that is phase-shift modulated with some continuous signal f will have the same waveform as one which is frequency-shift modulated with the derivative of f.  Likewise, a signal that is frequency-modulated by some signal f will have the same waveform as one which is phase-modulated by the integral of f.  Note that in some cases, it may not be practical to take the integral or derivative of f, so some signals can only be meaningfully represent phase modulation and others may only meaningfully represent frequency modulation.

Even though the waveforms of a frequency-modulated signal and phase-shift-modulated signal may look similar, however, there's often another important distinction.  Phase-shift modulated signals are often modulated relative to some other reference signal.  In some cases, the reference may be a signal sent on another wire.  In other cases, the reference may be a signal which was sent at an earlier time on the same wire.  In NTSC video, for example, every scan line starts with a few cycles of a 3.579545Mhz reference sine wave.  Colors later in the line will be encoded by waves that have a certain phase relationship to that reference wave.  Yellow, for example, will be represented by a wave whose phase matches the reference; blue will be represented by a wave 180 degrees out of phase.  Red and green are represented by waves +/- 90 degrees out of phase.  Note that all solid colors are be represented by the same frequency; the only difference between them is the phase relative to the reference wave.