My understanding is as follows:
- A Gaussian random walk is a Markov process $X_0,X_1,\ldots$, where $X_0$ has a Gaussian probability density function (PDF) and for $n=1,2,\ldots$, given $X_{n-1}=x_{n-1}$, $X_n$ has a Gaussian conditional PDF with mean equal to $x_{n-1}$.
- A Gauss-Markov process is a random process that is both a Gaussian process and a Markov process.
What is the difference between them? Are there Gauss-Markov processes that are not Gaussian random walks?