Can the kitchen screen show table orders and delivery orders on separate lists?

Not by type. The kitchen screen is one list in the order tickets arrived, whether they came from the counter, a table, the ordering page or a delivery app, because the cook works in arrival order. What you can split by is station: the buttons across the top show one station's dishes and hide orders with none of them. Each ticket says where it came from, so a table round and a delivery order are easy to tell apart on the card. The Tables, tabs and the kitchen screen tab in the docs describes the screen.