Yes it does. The captured group, now accessible with $1, does not include the quotes. The match does include the quotes. The full match (the equivalent of which gets highlighted in Vim) is accessible in $& (in Vim: \0). But the Perl snippet given only prints out the captured group because of the /g flag. See below.

In list context, if there are capturing groups, the match operator /.../g returns a list of all strings where the capture group matches.

"The /g modifier specifies global pattern matching--that is, matching as many times as possible within the string. How it behaves depends on the context. In list context, it returns a list of the substrings matched by any capturing parentheses in the regular expression. If there are no parentheses, it returns a list of all the matched strings, as if there were parentheses around the whole pattern."

http://perldoc.perl.org/perlop.html#Regexp-Quote-Like-Operators

This Perl is really saying:

for each place where ==([^=]*)== matches, print the captured match

Unlike Perl, Vim cannot access any captured groups outside of the search or substitute command. In other words, Perl can do stuff like this:

$mystr =~ /==(.*)==/;
print $1\n;

Vim cannot.

This is not a regex pattern thing. It's a language thing.

Yes, they both MATCH the quotes. But the capturing group only CAPTURES the text without quotes. The same is true in Perl.

Vim HIGHLIGHTS a match as if you're doing this in Perl:

print "$mystr\n" if ($mystr =~ /"([^"])"/);

Vim CAPTURES a group as if you're doing this in Perl:

$mystr =~ /"([^"])"/;
print "$1\n";

Note that the SAME pattern is used both times, but in a different way.

Not really. Vim has its own dialect. Although Vim regex can do a lot of what Perl's can, it's not a 1-1 match.

Not in the regex syntax. But as discussed it's not Perl's regex syntax allowing it to work in Perl either, it's how the regex is applied. Using the /g flag on a match operator in Perl gives you all matching substrings.

Vim can do something similar with the matchlist() function if you pass a count to it in a loop until the match fails. I'm not sure if there's a more efficient way to extract all matches or not.