You only think that both versions of your code use the same variable, but the second version does not. What happens in fact is, that your sub print_summary uses the global variable $type ($main::type, to be verbose), while you later on declare a lexical variable $type. The strict pragma tells you about that, which is why you should use it:

use strict;

sub print_summary {
    if ($type =~ /w/) {
        print "Hello\n";
    };
};

my $type = "w";
print_summary;
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Here, Perl raises an error that you're using an undeclared variable $type in print_summary, which tells you that declaring the variable too late prevents Perl from seeing it.