These words are used interchangeably, you need to specify exactly. The main distinction is does it have a MMU or not.
"Emulation" evolved to mean virtual machine, now people are denying that wine or xterm are emulators.
"Operating System" evolved to require virtual memory and paging, now people are denying that MS-DOS was an operating system.
"Microprocessor" evolved to mean computing chips with MMU, im waiting for people to deny that the 8086 was an microprocessor because it does not have an MMU.
The infinite shitcycle of people improvising language instead of researching.
https://web.archive.org/web/20150928042254/http://wiki.wineh...
I mentioned the shift of meaning to "virtual machine" in the post you replied to, please read it more carefully.
Emulation and Simulation are different in some regard: emulation is only imitating some aspect of a thing, while simulation imitates a thing by using (usually physical) models.
xterm is a VTxxx emulator, and VT simulator does look like this: https://www.pcjs.org/machines/dec/vt100/
I totally agree with your main point though that emulation is a broader topic than is generally thought.
Also, back in the day emulators emulated the CPU for sure, while an API implementation wasn't never called "emulation". Ever.