To avoid complicated nested loops, I'd make use of a hash to index your first file and then look up the second list of words in the hash. Here is something a bit more simple that you can mess with to fit your needs:

#!/usr/bin/env perl
use strict;
use warnings;
use feature 'say';

my $file_1 =
  "the cat ran up the tree the cat the dog then barked at the cat the 
+cat jumped out of the tree";
my $file_2 = "the cat dog";

my %words;
$words{$_}++ for split / /, $file_1;

say "$_: $words{$_} occurrence(s)" for split / /, $file_2;

__END__

the: 7 occurrence(s)
cat: 4 occurrence(s)
dog: 1 occurrence(s)
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