Covariance vs Autocorrelation
According to your definition of autocorrelation, the autocorrelation is simply the covariance of the two random variables $Z(n)$ and $Z(n+\tau)$. This function is also called autocovariance.

As an aside, in signal processing, the autocorrelation is usually defined as

$$R_{XX}(t_1,t_2)=E\{X(t_1)X^*(t_2)\}$$

i.e., without subtracting the mean. The autocovariance is given by

$$C_{XX}(t_1,t_2)=E\{[X(t_1)-\mu_X(t_1)][X^*(t_2)-\mu^*_X(t_2)]\}$$

These two functions are related by

$$C_{XX}(t_1,t_2)=R_{XX}(t_1,t_2)-\mu_X(t_1)\mu^*_X(t_2)$$