You could for example implement the criteria using these two rules:

1. A string is a true substring of another if the other string starts with something else
2. A string is a true substring of another if the other string ends with something else

Then you only need to find out how to construct an "or" condition for regular expressions and find implementations for "starts with", "ends with" and "something else".

See perlre for ideas on how to implement these.

If you just need a check, and it doesn't have to be a regex, then maybe index() and ne would work?

if( index($str1, $str2) > -1 && $str1 ne $str2 ){
    print "$str2 is a substring of $str1\n";
}
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With tests to make sure it works as expected:

#!/usr/bin/env perl
use strict;
use warnings;
use Test::Simple;

my $str1 = "helloworld";
my $str2 = "hello";
my $str3 = "hello";

ok( is_substring($str2, $str1), "str2 is a substring of str1");
ok( !is_substring($str3, $str2), "str3 is not a substring of str2");

sub is_substring {
    my ($substring, $string) = @_;
    return 1 if index($string, $substring) > -1 && $string ne $substri
+ng;
}
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Implementing the criteria given by Corion here, and just for completness, here's a single-regex solution. Note that this accepts the empty string as a substring of any non-empty string.