Very often WoC starts after DCA closes. The area around Paradise Lagoon will close even earlier than 8 to ensure that some attractions can be totally shut down before WoC starts.
When all Disney parks close, such as DL at 8pm. That means the lines for attractions close at that point meaning that no more people are allowed to line up. It doesn't mean the park is closed and everyone is kicked out. For example if Space at 8pm has a 120 minute wait, it will be running until 10pm. But when you get off there is not much do do except be thanked for visiting and waved goodbye.
At the 8pmclosing dining and shopping will close, but it's staggered. So it's not an all at once close down. Usually sit down dining will close, but things like pop corn carts will be open a little longer. Shops in the rear close first. In general the back of the park closes, so people are encouraged to mvoe toward the activity that is closest to the gates. In particular Main Street shopping stays open an extra hour, except when a special(private) event is happening at night.