Why X-process is called a process?

I have recently learnt about kernels in machine learning. And I have been introduced to many different processes e.g. Gaussian process, Wiener process. Now my question is why a set of functions has been named as a process? For example this is the definition of Gaussian process:

Let $\mu: X \to R$ be any function, $k: X \times X\to R$ be a Mercer kernel. A Gaussian process $p(f) = GP(f;μ,k)$ is a probability distribution over the function $f : X \to R$, such that every finite restriction to function values $f_X :=[f_{x_1},...,f_{x_N}]$ is a Gaussian distribution $p(f_X)=N(f_X;μ_X,k_{XX})$.

Which parts exactly associates to a process??