Suppose I use two functions and I denoted them by lowercase and uppercase letters $m(x)$ and $M(x)$. Of course, I have to distinguish them somehow.
How do I read this? Is capital/uppercase $M$ of $x$ and lowercase $m$ of $x$ ok?
Yeah, whatever makes you happy and is clear. I would personally, and I feel like this is the most common, read "big M of x" and "little m of x".
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I'd say "big em of ex" and "little em of ex". (I am spelling out "em" and "ex" so that I don't have to decide whether to write them uppercase or lowercase.)
In a situation where most other letters occurring were small, I might say "big em of ex" for $M(x)$ and "em of ex" for $m(x)$, but only if I were feeling particularly lazy; this inevitably seems to lead to confusion.