Is there any dictionary or similar for comparing and contrasting related/synonym words, such as for ex. "swing" vs "sway", or "ask" vs "inquire"?
A very nice book which seems to be exactly what you want is the following:
For a large number of words it analyses the nuances of the different synonyms.
To show you the book structure, I scanned an example page. You can see that for each key word there's a list of synonyms (the full word list can be found in the index at the end of the book), and for each synonym the text discusses its level of formality, its usage etc.
You'll need to scroll down past the definition-proper, examples, and etymology to get to this discussion, and not every entry has it. Note that M-W also has a Thesaurus tab, which takes you to a more traditional list of synonyms.
Off-line, many print thesauruses include similar kinds of discussion. Your local library or bookstore likely has a selection of these that you could browse.