Maybe "not the same thing" but definitely not "'keep checking for more matches'" (within the current when, anyway).

At least, not in the same sense as the /g modifier in a regex. Observe:

#!/usr/bin/perl
use strict;
use warnings;
use 5.012;
# 901284

my $count=0;
my $foo = "X x y y x y Z";

say "First, with a simple substitution '/g'";
my $simplecount = $foo =~ s/x/o/g;
say " \$foo: $foo; \n \$simplecount: $simplecount (i.e., 'x's changed)
+";
$foo =~ s/o/x/g;
say "\$foo restored: $foo \n";
say 'Now, with given/when and =~ /x/g';

given( $foo ) {
    when ( $foo =~ /x/g ) { 
           say "\$foo contains an x"; 
        $count++; 
        say "\$foo: $foo; \n \$count: $count;";
        continue 
    }
    when ( /y/ ) {
           say "\n \$foo contains a y"; 
    }
    default {
           say "$foo does not contain a y"; 
    }
}
say "\n Final \$count of 'x' in given/when matching 'x': $count";

say "\n $foo";
[download]

OUTPUT:

First, with a simple substitution '/g'
 $foo: X o y y o y Z;
 $simplecount: 2 (i.e., 'x's changed)
$foo restored: X x y y x y Z

Now, with given/when and =~ /x/g
$foo contains an x
$foo: X x y y x y Z;
 $count: 1;

 $foo contains a y

 Final $count of 'x' in given/when matching 'x': 1

 X x y y x y Z
[download]

One possible reading is that continue's precedence terminates the matching. Perhaps a wiser head will explain (and correct, as necessary).

Update: typo fixed (from /s/g to /x/g) at line 15 and in the output. Gnahh!