This is not a full answer to the question, as I don't feel I have anything helpful to say about any aspect of the situation except possibly the content of the post.
Firstly, thanks for posting that useful question.
Secondly, it does seem that the question would benefit slightly from a clarification, as Braiam's comments on the question rightly (well, he's the expert on that topic, not me) point out that the phrase "apt version" is somewhat misleading.
Thirdly, while I do think the edit to your question made it more accurate, I am not sure it made it more clear or more accessible. As you suggested in your question here, readers may be familiar with a "Snap vs. APT" debate (although your question does not pertain to that debate, I think) and Ubuntu users in particular are very likely to be using APT for package management. Since the question is not actually about packaging formats or package management, I think the original wording was probably just about acceptable. (I also think this probably makes the apt tag unnecessary (the question is not about APT itself)). I was not even sure myself that the snap version did not come from some Ubuntu snap repository of sorts and had to ask about it in chat.
Although I think both the original wording and the current wording are both more-or-less ok, I would like to suggest a wording for your question that avoids sort-of implying that APT has its own particular versions of software, rather than just happening to be the package manager most commonly called by users on the command line in Ubuntu to install software from the Ubuntu repositories (you can tell I'm struggling to come up with an accurate description that is actually readable) and also avoids omitting the mention of APT altogether.
How about this?
If I were to install the same application both as a snap and using APT, how would I be able to call each one separately and how would I know which one was running?
and for the title:
If I've installed an application both as a snap and via APT, how can I tell which one is currently running?