The following might surprise you:

use strict;
use warnings;

use Data::Dumper;

my @arr1 = ('a');
my $var1 = 'b';

my (@surprise) = grep($var1, @arr1);

print Dumper( \@surprise );
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Just re-read grep. Remember that grep uses a boolean filter - the first argument - to select values out of a list. Your 'filter' - $var1 - always evals to TRUE.

If seems that what you are looking for might be something like

use strict;
use warnings;

my @arr2 =('a', 'b');
my @arr1 = ('a');

my %reference = map { $_ => 1 } @arr1;

for my $var1 (@arr2) {
    print "match $var1\n"
        if exists $reference{$var1};
}
[download]

Hth.