Parse the file containing the smaller number of lines and build a hash. Then parse the larger file and match lines using a hash lookup:

use strict;
use warnings;

my $file1 = <<FILE;
applebananapearcarrotcarrotbeardeerdeer
goatcowduckswanchickenmouseratbirdmouse
chocolatedogdogfishmousecatdeerbird
newyorkcalifornianewjerseymousecatdeerbird            
FILE

my $file2 = <<FILE;
monksbicyclewindbikecars
computercomputerprinters
hellicopterairplaneshelf
chocolatedogdogfishmouse
printerprintermousecouch
FILE

my %f1Lines;

open IN, '<', \$file1;
while (<IN>) {
    my ($key, $tail) = m/(.{24})(.*)/;
    
    push @{$f1Lines{$key}}, [$tail, $.];
}
close IN;

open IN, '<', \$file2;
while (<IN>) {
    my ($key, $tail) = m/(.{24})(.*)/;
    
    next unless exists $f1Lines{$key};
    
    my @matches = @{$f1Lines{$key}};
    
    print "Line $. of file2 ($key$tail) matches:\n";
    print "   line $_->[1] of file1 ($key$_->[0])\n" for @matches;
}
close IN;
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Prints:

Line 4 of file2 (chocolatedogdogfishmouse) matches:
   line 3 of file1 (chocolatedogdogfishmousecatdeerbird)
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