There is little in common between the two.
Any set of numbers can have a mean. A z-score the standardised version of the Gaussian (or Normal) distribution. If X is a random variable that is normally distributed with mean µ and variance σ2 then
Z = (X - µ)/σ is distributed with mean 0 and variance 1.
Z is said to have the Standard Normal distribution. The value of Z is the z score for the random variable X..
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No.
The difference between arithmetic and geometric mean you can find in the following link: "Calculation of the geometric mean of two numbers".
Common Difference means the difference between two numbers.
If you mean the difference between -11 and 2*(-11), then it's 11.