__FILE__ is the file name that the __FILE__ token is in, and $0 is a variable containing the name of the program, as given to the shell.

They can most certainly be different - one case that comes to mind is a __FILE__ token in a library called by your program, but there are many others, particularly since you can assign to $0 (with varying effects on different OS), but you can't meaningfully assign to __FILE__.

Example code:

File 1 - firstfile

#!/usr/bin/perl -w
use strict;

print $0 . "\n";
print __FILE__ . "\n";

do 'filetwo';
[download]

File 2 - filetwo

#!/usr/bin/perl -w
use strict;

print $0 . "\n";
print __FILE__ . "\n";
[download]

It's simplistic, but should show the basic concept.