According to this answer there is no difference between tags and categories in terms of SEO. (In reply to your initial question.)
Since technically categories and tags are very similar, I assume that Google would also not see a difference between using built-in or custom taxonomies.
You can make your tags hierarchical and organize them in groups, but it’s more for usability than SEO. Of course, making your site more usable and increasing the click-through rate and the time that users stay on your site are also important ranking factors. So I conclude that it does make a difference, although not a huge one.
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