# %b is a hash already containing the values from fileB, with the 
# first column as keys and the second column as values.
# $file_of_matches is a file descriptor opened to one output file
# $file_of_misses is a file descriptor for the other output file
open my $fileA, '<', 'fileA' or die $!;
while( my $line = <$fileA> ){               # get a line from fileA
  chomp $line;
  my( $k, $v ) = split /\t/, $line;         # split the line on tab
  if( $b{$k} ){                             # do first columns match?
    if( $b{$k} =~ /$v/ or $v =~ /$b{$k}/ ){ # does one second column value contain
                                            # the other as a substring?
      print $file_of_matches "$line\n";     # yes, so print it to the match file
      next;                                 # and loop to the next line
    }
  }
  print $file_of_misses "$line\n";          # no, so print it to the non-match file
}