I've recently taken a great interest in the hyperbolic trigonometric functions and hyperbolic geometry in general and I've noticed that some definitions for the hyperbolic trigonometric functions involve "$z$" as the independent variable symbol instead of the standard "$x$" used in lower mathematics. Why? Here, take a look at Wolfram's definition for $\tanh$: $$ \begin{align} \tanh(z)=&\frac{\sinh(z)}{\cosh(z)}\\ =&\frac{e^z-e^{-z}}{e^z+e^{-z}}\\ =&\frac{e^{2z}-1}{e^{2z}+1} \end{align}\\ $$ (Source: Wolfram MathWorld: Hyperbolic Tangent)
This by no means seems to be the standard as Wikipedia uses the same definition but with an "$x$" instead of a "$z$". (Source: Wikipedia: Hyperbolic Functions) Perhaps this redefinition on Wolfram's part is merely a stylistic choice, after all, I am no mathematician. My personal theory is that the "$z$" denotes some relation to complex numbers or its complex graph as I sometimes see "$z$" used in those sorts of places. Are there specific guidelines or am I being quite silly and pedantic?
This is often used as a notation for a complex number $x + i y$. Other than the common use of letters near the end of the alphabet, the names of variables are pretty arbitrary.