Can someone explain the point of the lexical subroutines? [1]

In particular, I'm lost on the difference between

    sub outer {
        my $closurevar;
        my $inner = sub {
            ... use $closurevar...
        };
    }

and

    sub outer {
        my $closurevar;
        my sub inner {
            ... use $closurevar...
        }
    }

(I mean this as an honest question. That said, I do hope that I'm missing something and this is more than just a syntax gloss.)

[1]: http://search.cpan.org/~rjbs/perl-5.18.0/pod/perlsub.pod#Lex...