One problem is that you are trying to split the filename, not words in a file. When you want "unique", think "hash".

use warnings;
use strict;
use Data::Dumper;

$Data::Dumper::Sortkeys = 1;

my %words;
my $tot = 0;
while (<DATA>) {
    for my $word (split) {
        $words{$word}++;
        $tot++;
    }
}

print Dumper(\%words);
print "The number of words in the file is $tot\n";

__DATA__
a b c
d e 
f g h
a b c
[download]

prints...

$VAR1 = {
          'a' => 2,
          'b' => 2,
          'c' => 2,
          'd' => 1,
          'e' => 1,
          'f' => 1,
          'g' => 1,
          'h' => 1
        };
The number of words in the file is 11
[download]

• use strict and warnings
• Basic debugging checklist
• If you don't like the Data::Dumper output, read sort and perldsc.