> But by definition, different types of spaces all have to look exactly the same when rendered as text.

Only in the sense that they look like nothing at all. They can, however differ in how much nothingness they represent [1] which I would argue can make them look quite different one another.

[1] https://en.wikipedia.org/wiki/Whitespace_character#Unicode (Feel free to ignore tabs, line breaks and other characters that don't feel space-y enough. There should still be plenty left to choose from.)