Isn't "while" suppose to be the opposite of "until"?

Yes, but you want the “opposite” (actually, the negation) of unless, which is simply if. See perlsyn#Statement-Modifiers.

But there is another problem: $1 refers to the first capture in the most recent regular expression match. In the expression:

$B .= "$1\n" unless $1 =~ /def/;
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the concatenation $B .= "$1\n" occurs only if the regex match $1 ~ /def/ fails; in which case, there is no match, so the most recent match is still the one from the while loop regex. But in the expression:

$B .= "$1\n" if $match =~ /def/;
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the concatenation occurs only if the new match succeeds; in which case, $1 is overwritten. You can fix this by assigning the value of $1 to a temporary variable:

while ($A =~ m{(.+)}g)
{
    my $capture = $1;
    $B .= "$capture\n" if $capture =~ /def/;
}
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Hope that helps,