I mean the first. It breaks when you enable "extend desktop" or "extend these displays" in Windows while Spine was running while you originally had the setting at "show desktop only on *"/"pc screen only".
(I don't always have my second monitor on. Weird, right? XD)

Yeah, my card's from the red team. XD

Just to clarify the steps.
(1) Have two monitors on your system.
(2) Set to Single monitor mode (in Windows 8, this is phrased as "PC Screen Only").
(3) Run Spine. Let it finish loading.
(4) Switch to Dual-monitor mode.
At this point, there should be a black rectangle where the window used to be.
Note that you can move the window but clicking or moving it doesn't fix the display, although it does still seem to respond correctly.
Clicking on the area where the X button should be does close Spine.

Optional steps:
(5) Minimize using the taskbar.
(6) Restore the window using the taskbar.
At this point, there should be a teeny tiny Windows 98-looking titlebar. Clicking on the buttons does nothing.

A workaround I just learned right now:
(5) Move your cursor to the edge of the rectangle and click-drag to resize the window. Resizing seems to return the window to normal.

I wouldn't call this a huge deal though. Just something to note when you're fond of switching modes like a weirdo (eg, pharan)

Oh, I was talking about the phrasing on the Win + P menu that appears on the right side.

I see. Well, if someone runs into the same issue, at least they'll have some info. I doubt people will actually run into this problem and be frustrated though.