Nothing stops two playlists being eligible on the same screen at the same time, and it happens more often by accident than by design.
They share the screen
The screen cycles through every eligible playlist, giving each its turn, then comes back to the first.
That is often what you want. A permanent playlist of company notices and a temporary playlist for an event both run, and the screen alternates without either being switched off.
The order is alphabetical
Playlists on a screen play in order of title. That is the only lever you have over rotation order, and it is a real one.
If order matters, number the titles: 1 Welcome, 2 Safety, 3 Notices. Without that, Announcements plays before Welcome because of how the alphabet works, not because anyone decided it.
This makes renaming a playlist a scheduling change on a screen showing several. Worth remembering before tidying up names.
Priority does not share
A playlist marked priority takes the screen exclusively while its schedule is active, and everything else waits. See Priority override.
When nothing is eligible
A screen with no eligible playlist has nothing to show. A screen that goes blank at 18:01 is a schedule ending, not a fault, so check the schedules before checking the device.
Keeping this simple
Overlap is a legitimate tool and a common source of confusion. The two arrangements that stay understandable are one playlist per screen with a schedule that switches content, or several playlists deliberately sharing, with numbered titles.
The arrangement that causes trouble is several playlists overlapping by accident because their schedules were written separately. The effective schedule summary on each playlist is the way to catch it. See Scheduling.