Why are there two kinds of formula for Probability Generating Function?

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In this link:

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On the other hand, in this link:

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So, how are these two equations same?

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The first link gives the formula for moment generating function. $M_X(t)=E[e^{tX}]$

The second link gives the formula for probability generating function for discrete random variable. $G_X(s)=E[s^X]$

They are not the same.