How do I get term data associated with the current post, where the result is not wrapped in HTML?

OK, so let’s make it straight:

get_the_term_list

Returns an HTML string of taxonomy terms associated with a post and
given taxonomy. Terms are linked to their respective term listing
pages.

So it will generate HTML code and return it as string.

get_terms

Retrieves the terms in a given taxonomy or list of taxonomies.

So it has nothing to do with current post.

get_the_terms

Retrieve the terms of the taxonomy that are attached to the post.

So this is the one you’re looking for, I guess.

It will get the terms of given taxonomy that are assigned to given post and return them as array – so you can iterate it and do whatever you want with them…