The header function is used to send raw HTTP headers back to the client: PHP header function
<?php
header("HTTP/1.0 404 Not Found");
?>
The above (taken from the PHP documentation) sends a 404 header back to the client.
The include function is used to include files into the current PHP script (the same as require) PHP include function
vars.php
<?php
$color = 'green';
$fruit = 'apple';
?>
test.php
<?php
echo "A $color $fruit"; // A
include 'vars.php';
echo "A $color $fruit"; // A green apple
?>
This example (again from the PHP documentation) includes the vars.php script in the test.php script and, after the include, allows the test.php script to access the variables declared in the vars.php script.