For the difference between $var and $::var see the following code:

package Foo;
$var   = "hello\n";
$::var = "bye\n";

print $var;        # hello
print $Foo::var;   # hello
print $::var;      # bye
print $main::var;  # bye

package main;
print $var;        # bye     !!
print $Foo::var;   # hello
print $::var;      # bye
print $main::var;  # bye
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So - as mentioned elsewhere - $::var is equivalent to $main::var while $var refers to the $var variable in the current package.