If you don't give a value to the variable, then its value is undefined, which is different from having the empty string as value.
The list notation ($var) is normally used to declare several variables at once, like in

my ($a, $b, $c) = (1, 2, 3);
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The first and third line in your text have the same effect, and the second and fourth line have the same effect.

my $a;
my $b = "";
print "\$a is not defined\n" unless defined $a;
print "\$b is defined\n" if defined $b;
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daniel.