Edit: This is a bug
After a restart, normal behavior returned.
Also, I noticed some files that appeared on the external display momentarily and disappeared. These files only showed from a Finder window showing the Desktop but did not show on either Desktop (aside from showing for a second when switching Desktops).
When using an external display (not mirroring), I cannot focus on the Desktop (by clicking on it) or drag files to it.
If I have an App open there, clicking anywhere on the screen will simply keep the focus on the latest App and will not switch to the Finder. Dragging a file to the external Desktop simply bounce back.
Cannot say if it's a High-Sierra thing or earlier, or whether it's an expected behavior.