I'm gonna disagree with this comment here.
not sure where that definition is from but it seems to be using the word 'or' to mean either of these rather than saying you need both.
i.e. you could still be aro, even by that definition, if you have interest but no desire.
I dont think saying you must have neither desire nor interest to be aro is a sensible idea. interest seems such a broad word. For example consider a lesbian, is she no longer a lesbian if she is 'interested' in hetrosexual relationships. that seems stupid, there are plenty of reasons to be intersted in those relationships which have nothing to do with her lesbianism. perhaps curiosity, perhaps because those are the relationships most people she knows are in and good sense says she might want to try to understand them. perhaps studying how different sorts of people make their lives work is interesting in its own sake.
I certainly prefer the way AUREA's glossary defines aromanticism:
Commonly describes someone who experiences little to no romantic attraction, abbreviated to aro.
It also describes someone whose experience of romance is disconnected from normative societal expectations, due to feeling repulsed by romance, or being uninterested in romantic relationships.
I'm not going to say its perfect but that seems a lot better than only allowing people who have absolutely no interest at all in the way most of humanity seem to lead their lives.
also wtf is that bit in the middle, I have no idea what is going on there.