It has been a long, L--O--N--G time, but I think the Windows Clipboard was a service that maintained a limited-depth LIFO cache of OLE/COM objects of varying types that implemented some sort of clipboard Interface so that standard cut/copy/paste application code could interact with it. The clipped object could present different Interfaces so that a given clip might post plain text. an image, or other things, depending on what format the receiving app requested.
However under Unix and Linux, things were never so tidy. For one thing, the GUI is
optional on Unix-like OS's, so the abilities required for any sort of cut/paste on a strictly command-line systeem are not the same as one that's running apps in a GUI. And please realize that since the windowing on Unix-like systems is plug-replaceable (X, Wayland or even PostScript on the NeXT system) as well as the desktop manager (Gnome, KDE, Cinnamon, XFCE, and so forth), the GUI-oriented clipping interface is also not defined by a unified standard. The *n*x world is a lot less consistent in UI design and function that Microsoft Windows is.
However, this is a good overview:
https://www.baeldung.com/linux/clipboard
The clipboard's internal organization is a black box, and it often only allows a single object, not a LIFO. If it does support a LIFO, it's generally a shallow one. and if you push too many items, the oldest ones fall off and are lost. I won't call it a stack for semantic reasons, even though stacks can implement LIFO.