Well, I think the first thing to realize is that language is a terribly imprecise way of communicating. When it comes to terms that are relatively recent additions to a cultural lexicon this is especially evident. So don't be surprised to see people with wildly different ideas about what these terms "mean".
For me, a relationship describes any interaction between people. But that's obviously not how you see the term. Your term "relationship" I suspect is more similar to what I would call a "committed, likely monogamous (or stated monogamous), romantic, and sexual relationship." See how much more time it takes to be precise?
The difference, for me, between the NSA and FWB relationships is the notion of commitment (and note that I do not
see that as synonymous with monogamous, or "loyal"). A FWB relationship does have a friendship, plus a romantic and/or sexual component. I believe that there is usually a commitment to continuing the relationship, ie, staying friends. An NSA relationship is more like people who meet and decide to have sex without any consideration for maintaining contact, sexual or otherwise. Of course, an NSA situation can be ongoing, but it still revolves around sex, not an interest or liking of another person. But to further confuse matters, either of these types of relationships can change into the other, or into another relationship form altogether. I think both types are often expected to by non-monogamous but not always, and that's an area where people, if they don't communicate, can arrive at some misunderstandings about the nature of the relationship.
I would also point out that relationships can be far more diverse than the categories that are commonly discussed and that leads to confusion because people seek a label to put on their experience. Many of my relationships have not fit either of those labels, and yours may not either. So, if the labels are causing misunderstandings between people perhaps discussing perceptions and expectations without the labels might be helpful.