Why is it forbidden by the IEEE to post 'author-submitted' papers on ArXiv?
what is the logic between allowing preprints, but not author-submitted papers?


There is no logic behind this. It is part of the culture of publishers who want to restrict access as much as possible, so they can profit from selling closed-access research.

If it were just up to publishers, I don't think IEEE would allow preprints, either. But they make an exception for arXiv because the culture has changed such that people want to make their papers available there. Additionally, note that it is valid to post any version of your paper other than the final copy-edited version online on your website.

(Note: if you ask IEEE, they might come up with some reason for it. Perhaps they treat submitting to arXiv as a competing submission, and since you can't submit elsewhere while a paper is under review, you shouldn't be able to submit to arXiv either. But I don't think this objection holds water, because arXiv and posting to a personal website have similar effects. Also, I don't think it is the real reason, which is that their business model relies on limiting paper access to some extent or another.)


  What is confusing me is that IEEE differentiates between preprint and author-submitted paper, where it is okay to put a pre-print on arXiv, but not okay to put the author-submitted version.


It's worth pointing out that many researchers do wait to publish online until a paper is accepted. The idea is that papers go through lots of revisions, and the title, narrative, and main results of a paper could change after it goes through the publication process (possibly being rejected a few times). So, you may not want people to read the draft version and get a bad idea (or wrong idea) about where your work fits, and you prefer to make only the most impressive and clarified version available.


  how much difference does there have to be between the two versions to not count as the same?


There is no rule here, as far as I know. It could even be the same version, but that probably means you ignored the reviews, which is a bad thing. Often for my papers, there is also zero difference between the preprint and the "final" version, other than it having a new template and formatting to look pretty, which doesn't really matter. (And I prefer to treat the preprint as the real "final" version.)