Definition of Stationary Increments

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What is a simple definition of Stationary Increments?

I saw that: $X_t - X_s = X_{t-s}$

How does this relate to the property of being a stationary process? Or even a weakly stationary process, that:

$E(X_t)=0$ and $Cov(X_t, X_{t+u})$ is a function of u