So for most of my school years I never used the divisor sign(/), instead opting for putting a number above the other, with a horizontal line in between. Just to be sure, "/" is division, right?
For 'similar' I never used/saw two wavy lines used, instead I put two adjacent dots above the equal sign. And so on...
Why is there a regional discrepancy in mathematical symbols?
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Mathematicians can't even agree on what is a natural number and what is a whole number. As long as (the writer) is consistent and explains, at the very least by context, what they mean, then we have to give them their freedom of expression. We expect the notation to be lucid and amenable to the problem being solved. If not, then the author has failed to communicate.
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You can find the history of the various symbols used for the division in this instructive Wikipedia entry. It shows in particular that the variations in notation are not only regional but also domain dependent. For instance, the slash is used in most computer languages.
There is indeed a large variety of symbols used by mathematicians and if you need more symbols, you can refer to the The Comprehensive $\LaTeX$ Symbol List, which might explain why there is so many different notation around...
Mathematical symbols vary regionally for the same reason that, say, language or in units of measurement do. Standards and conventions are only every established locally, and will only be adopted elsewhere if there is a motivation to do so. Using the example, whether the world should use the symbol $\approx$ or $\ddot =$ in some context simply isn't worth fighting for when both unambiguously convey their meaning in the texts that use them.
Beyond that, mathematical notation isn't even "regionally" consist. People adopt different notations constantly based on what they feel will convey their ideas most clearly. I myself will use the symbol $f^n$ to denote a host of different ideas, and will use entirely different symbols to represent those ideas when the context could make them ambiguous.