i don't have the mathematical definition at hand, but i'll give it a shot. hopefully that helps.
i'd say steady state means that if you have a state x[n'], its steady state iff x[n+1] = x[n] for all n >= n'.
contrary to that, stationary is a statistical description. if you have a random process, then its strict sense stationary iff f_n(x) = f(x) for all n, where f_n(x) is the pdf for the nth realisation. that means that the pdf is the same for every realisation (realisation can be for example a time instance). wide sense stationary means the same thing but for the first two moments, i.e. mean and variance, instead of the full blown pdf.
in other words, for a steady state the actual value doesn't change any more in the future, but for a stationary process just the distribution (or first two moments) of the values is the same for every time instance.
Fig 32.6 Steady and unsteady mean motions in a turbulent flow