The alias really is an alias for the existing class. It's not a new class of any kind - whether by inheritance or otherwise; it doesn't just look and behave exactly like the existing class; it really is the same class.
<?php
class foo
{
public static $count = 0;
}
class_alias('foo', 'bar');
bar::$count++;
echo foo::$count; // Output: 1
echo get_class(new Bar); // Output: foo
?>
Note in the last line there that aliases are just as case-insensitive as "genuine" class names.