That page you referenced isn't quite right. The m// operator never returns the number of matches. In scalar context, it returns true (1) if the match succeeds or false if it doesn't. In list context, it returns a list of matches, which you can turn into a count by passing it through an anonymous list:

#!/usr/bin/perl
use Modern::Perl;

my $str = 'thisthis';

my $n = $str =~ /this/g;
say $n;
$n = $str =~ /that/g;
say $n;
($n) = $str =~ /this/g;
say $n;
$n = () = $str =~ /this/g;
say $n;

#output
1

this
2
[download]

The s/// operator, on the other hand, does return the number of matches, regardless of whether it's called in scalar or list context.