Difference between $f(.)$ over $\mathbb{Z}_q$ and $f(x)$ for $x \in\mathbb{Z}_q$

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What is the difference between the two following notations.

  1. function $f(.)$ over $\mathbb{Z}_q$ .

  2. function $f(x)$ where $x$ takes values from $\mathbb{Z}_q$

I think that both are same. Is there any difference between the two notations?