What is the difference between phase noise and frequency noise?
Phase Noise and Frequency Noise are not two different noise sources, they are artifacts of the same noise, it is just a matter of what units you want to use.  Frequency and Phase are directly related as frequency is phase changing with time, so if you have one you will always have the other; frequency and phase are related by derivatives and integrals: the derivative of phase equals frequency  (as a change in phase versus time is frequency). 

For a waveform in the time domain that represents the frequency changing with time as $f(t)$, the equivalent function as phase changing with time would be:

$$\phi(t) = \int f(t) dt$$

And likewise to go from phase to frequency:

$$f(t)= \frac{d\phi(t)}{dt}$$

Note this can be very confusing as we are talking about a waveform whose value represents frequency changing with time; so to be very clear this waveform I am describing is indeed in the time domain (as the independent variable is time), and we are observing how the frequency changes versus time. We can take the Fourier Transform of this waveform, and then observe the rate of change of frequency (which is the frequency of our frequency variable....even more confusing!).

However getting that straight is important to understanding the difference between Phase Noise and Frequency Noise: 

Integration in the time domain is a low pass filtering response in the frequency domain, as indicated by the Laplace Transform property for integration:

$$L\{ \int x(t)dt\}=\frac{1}{s}X(s)$$

And similarly the derivative in time results in a multiplication by s in Laplace, which represents a high pass function (as you can get the frequency response (or Fourier Transform) for both by setting $s=j2\pi f$)

Therefore a Phase power spectral density and Frequency power spectral density are related as follows:

$$S_f(f) = (2\pi f)^2 S_{\phi}(f) $$

Where $S_f(f)$ is the power spectral density due to frequency fluctuations, and $S_\phi(f)$ is the power spectral density due to phase fluctuations. 

For example, if you had a white frequency noise process (meaning the FREQUENCY power spectral density was flat for all frequencies), the PHASE power spectral density would be going down at the rate of $1/f^2$ or 20 dB/decade.

Here is a plot I have showing the relationship between Phase Noise and Frequency Noise as time domain plots. Notice how the phase is smoother but wanders off relatively slowly with varying random offsets (low pass with random walk), while the frequency plot has higher frequency content but does not deviate from 0 for long durations (high pass filtered).