Googling for "Math squiggle that looks like a cursive P" is not a very elegant or convenient way of learning new symbol names.
I wish every proof or equation came with a little table that gave the English pronunciation and some context for each symbol used.
It would make it a lot easier to look up tutorials & ask questions.
All of those you're of course expected to properly distinguish in handwriting.
I'm sure most of them have some sort of canonical name, but I'm usually tempted to read them with different intonations.
(Oh and of course each of those needs a separate Unicode character to preserve the "semantics". Which I imagine is thrilling edgy teenagers in YouTube comments and hackers looking for the next homograph attack)
"Fake-Handwritten R" is an extra fancy calligraphic version which is not hard to distinguish. The Fraktur R is a pain to write, but you can write an upright "Re" as an alternative.
The basic issue is that using single symbols for variables is very convenient (both more concise and less ambiguous than writing out full or abbreviated words when writing complicated mathematical expressions), but there are infinitely many possible variables and only a small set of symbols.
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1. I would put Donald Knuth in that category, given his choice to not include blackboard bold in his original inventory of characters for Computer Modern, but that might just as much have been a choice based more on limitations of the computing systems he was working with at the time (or his needs for typesetting The Art of Computer Programming which were the primary driver of TeX).
As for "where things are going" – this has been changing extremely gradually over the past 60 years. If the trend accelerates maybe you'll stop seeing both variants in wide use in about another century.