'halt' would work just as well as 'kill' but the latter sounds cooler. It's OK to use jargon within a professional context, but using it without regard to one's audience is generally obfuscatory.

The latter isn't used because it sounds cooler, it is literally rooted in the "kill" command on UNIX systems of old. The kill command is still used today, but can be used to send signals to running applications aside from "please exit immediately".

If you want to get really nitpicky, halt isn't as absolute and precise as kill. Halt can mean that the app's activity is simply paused, but its resources are still held and it can in the future be resumed from its original position. Kill very much and in no uncertain terms means to immediately terminate the execution of an application without further processing of the current task.

They really aren't interchangeable terms. If you are talking about interchangeability to an end-user who doesn't have such knowledge, I would argue even then some users may understand the different between not using an app and actually terminating it. Such as halting a video vs closing the window. If you are looking for analogies of proof of understanding, people say to "kill the engine" or other mechanical devices. So again, the term "kill" used in reference to terminating things isn't that weird.

The individual who was surprised to hear of killing an app could have been surprised for a variety of reasons, but not in such a way that I think "halt" should be used over kill.

"Halt" isn't strong enough. You aren't just making it pause wherever it happens to be, you are getting rid of it.

Halt used to mean absolute termination rather than a pause, as in The Halting Problem. This was still used as the canonical term in UK computer terminology when I was growing up, but it may be different elsewhere.

Isn't "absolute termination" the Unix meaning of "halt" as well?

I thought so but others seem to disagree.

I don't disagree about its technical meaning, but this entire debate is about what it OUGHT to be so that NON-technical people have an easier time.

In that respect, "kill" is probably better, since it accurately conveys common ideas like "irreversible" and "messy".