local($x) saves away the old value of the global variable $x, and assigns a new value for the duration of the subroutine, which is visible in other functions called from that subroutine. This is done at run-time, so is called dynamic scoping. local() always affects global variables, also called package variables or dynamic variables.

my($x) creates a new variable that is only visible in the current subroutine. This is done at compile-time, so is called lexical or static scoping. my() always affects private variables, also called lexical variables or (improperly) static(ly scoped) variables.

For instance:

 sub visible {
    print "var has value $var\n";
    }
    

 sub dynamic {
    local $var = 'local'; # new temporary value for the still-global
    visible();# variable called $var
    }
    

 sub lexical {
    my $var = 'private'; # new private variable, $var
    visible();# (invisible outside of sub scope)
    }
    

 $var = 'global';
    

 visible(); # prints global
    dynamic(); # prints local
    lexical(); # prints global
    

Notice how at no point does the value ``private'' get printed. That's because $var only has that value within the block of the lexical() function, and it is hidden from called subroutine.

In summary, local() doesn't make what you think of as private, local variables. It gives a global variable a temporary value. my() is what you're looking for if you want private variables.