Looks like you want to compute the Hamming distance (number of character positions in which they disagree) between two words. Do you really really need a regex, or will another way of matching be ok?

If you're not strongly committed to using a regex, use something like this (probably will do strange things for non-ascii character sets):

sub hamming {
  my ($x1, $x2) = @_;
  return -1 if length($x1) != length($x2);

  (my $xor = $x1 ^ $x2) =~ tr/\x0//cd;
}

print hamming(@$_), $/
   for [qw[ abcdef abccef ]],
       [qw[ abcdef abc ]],
       [qw[ abcdef abbbbf ]];
__END__
1
-1
3
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However, you could still cram this hamming function inside of a regex, with some trickery/cheating:

# untested
my $target = "abcdef";
my $distance = 1;

my $len = length $target;
my $qr  = qr/ \b(\w{$target})\b (?(??{ hamming($target,$1) < $distance
+ }) | (?!))  /x
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I'm in a bit of a rush at the moment, so my (?(cond)pattern) syntax is probably wrong. Also, it could be optimized greatly to avoid backtracking (say, with (?>pattern) to capture $1). Maybe someone can help me out here with the details, but this should give some idea..