The charge is $6 per day. Upon paying at first park, you will be given a pass that allows you access to other parking lots, that is, if you park hop, for that day only. Visit the same or different park the next day, and the charge is $6
Just clarifying "park". You would pay one amount to park at any of the theme parks and can move your car around that day.
As for valet parking, you would pay the $6 at your first valet and then have a hang tag that shows you paid at the next resort where you might valet park.
Your payment at a theme park lot would not count towards a valet parking or vice versa.