What is the point of "extended" digits like ۱

This stack exchange comment uses the ۱ character, which I had never seen before. Using babelstone, I've identified the character:

U+06F1 : EXTENDED ARABIC-INDIC DIGIT ONE

Now, the interesting part to me comes when using search functions in Chrome. If I type ۱, it matches all 1 characters. That's similar behavior to é and e. One shows up when the other is searched (in many languages).

I understand generally the relationship between é and e, where there are modifications of pronunciation and can even be different letters entirely, depending on the language. But how does ۱ relate to 1? Presumably it's different enough in concept to warrant a new unicode character rather than a font choice.

Solution 1:

Even a few minutes after posting this question, I feel a bit foolish for asking, because the "point" of this Arabic-Indic character is simply to represent Arabic script. Upon seeing the word Arabic in the description of the character, I was conflating the Euro-centric idea of Arabic Numerals used in Western languages like English with Arabic script itself.

So the relationship between ۱ and 1 is that they represent the same concept, but in different scripts entirely. As Gantendo links in the comments, fallback substitutions use this conceptual relationship to map the idea of "one" across different scripts. A "vertical metric" as Microsoft puts in Gantendo's link