Hey there, hi there, Stewart! Thanks for your question.
When you are looking at the
Walt Disney World website, and it says "valid theme park admission" or "valid admission," it basically means that you have to have a
theme park ticket. Whether you have an annual pass, a regular single or multiday theme park pass, a military ticket - it just means any type of admission medium that allows you access into the theme parks.
On top of the valid theme park admission, you now also need a
theme park reservation. You have to have a reservation - plus your valid admission - to get into any of the Disney theme parks. Even if you are just going in for a dining reservation, both of those things are necessary to gain entry.
The only time you would not need both of those things would be if you have a
park hopper option on your theme park tickets. The park hopper option allows you to switch to a different theme park after 2 PM, but it does not require a separate theme park reservation. You'll just need the park reservation for your first park of the day.
Hopefully, this clears up any confusion for you, Stewart!
Anna