I believe what you're trying to do is replace words without also replacing words which contain the original words. Or to put it another way, you want each word bracketed by word boundaries.

Thankfully for you, there's an easy way to specify this: \b

my $x = 'a';
my $y = 'b';

while (<DATA>) {
    chomp;
    s/\b$x\b/$y/g;
    print "$_\n";
}

__DATA__
a
a 
 a
 a
[download]

Incidently, use of $a and $b is not recommended, since these are used in sorts.