What is the difference between Perl's ( or, and ) and ( ||, && ) short-circuit operators?

Which of these subroutines is not like the other?

sub or1 {
    my ($a,$b) = @_;
    return $a || $b;
}

sub or2 {
    my ($a,$b) = @_;
    $a || $b;
}

sub or3 {
    my ($a,$b) = @_;
    return $a or $b;
}

sub or4 {
    my ($a,$b) = @_;
    $a or $b;
}

I came to Perl 5 from C and Perl 4 and always used || until I saw more scripts using or and I liked the way it looked. But as the above quiz shows, it's not without its pitfalls for the unwary. For people who use both constructs or who use a lot of or, what rules of thumb do you use to decide which construct to use and make sure the code is doing what you think it is doing?