Why the Perl regular expressions are not having mathematical sens; but grep's regex have?

I saw here that the Perl regex are not based on the mathematical sense; while the grep tool (i.e. Basic one) had basis in the mathematics.
Have found this stated (in the second link above), that the Advance version too lacks mathematical sense.
But, the link of grep here, does not state anything, about the difference of the Basic one with the Advance one.