The first doesn't change the value of $a.

There is no difference between the string created by the literals '' and "".

undef is nothing like the empty string. It's a completely different value. Your confusion probably arises from Perl automatic conversion between data types. When you try to use undef as a string, it evaluates to the empty string and issues a warning. When you try to use undef as a number, it evaluates to zero and issues a warning.

The number zero being automatically converted to a string:
>perl -wle"my $x = 0; print $x"
0

Undef being automatically converted to a string:
>perl -wle"my $x = undef; print $x"
Use of uninitialized value in print at -e line 1.
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