It's the former thing. Generally speaking, Daedra are usually considered to be entities that didn't take part in creating Mundus, whereas Aedra are entities that did. But the categories were hardly finalized at that point of deciding to join in on the fun of making Mundus or not.
There are plenty of examples of beings who could be Aedra but are classified as Daedra.
For one thing, the entire race of the Magna Ge including Magnus left Mundus partway through the process, so whether they count as Aedra is contentious. Most mer consider Magnus to be an Aedroth, and maybe they consider some other Magna Ge to be Aedra too, whereas most men don't include the Magna Ge as proper gods and don't give them much thought; they mostly only care about the Divines, the Aedra who were powerful enough to become planets, and Lorkhan. The Daedric Prince Meridia was a Magna Get, but she's considered a Daedroth by most people. So it's not clear what the reasoning is for classifying Magna Ge as Aedra or not. Maybe some elves are descendants of Magnus but Meridia doesn't have any descendants? Or maybe it's just that Meridia hangs out in Oblivion which makes her "bad" by association.
Then there's the case of Lorkhan. Because the term 'Aedra' is a merish term which means 'our ancestors', and mer don't claim descent from Lorkhan since as far as we know he didn't reproduce at all, and he supposedly betrayed the Aedra, he's usually considered to be a Daedroth by them. Also, Lorkhan was techincally able to survive since his heart was unable to be destroyed, and Mankar Camoran pointed out that unkillability is a trait that Daedric Princes have but not Aedra because they gave up too much of their power. However, since men like Lorkhan, even if they don't claim descent from him, they tend to see him as an Aedroth; plus Lorkhan did contribute a lot to the creation of Mundus before he died. And yet other people argue Lorkhan should be considered his own thing. As you can see, it's a hot topic of debate.
Finally, Trinimac is considered to be an Aedroth, and Malacath is considered a Daedroth, even though supposedly Malacath is Trinimac. So why everyone classifies them this way is a strange logic. If Malacath is Trinimac then Malacath should be an Aedroth too, unless Malacath isn't really Trinimac but instead a being that was "born" or warped from him somehow. ¯\_(ツ)_/¯
So even though there is supposed to be a rigid distinction between Aedra and Daedra, the division isn't so clear-cut, and the mortal races are more than happy to fudge the definitions depending upon whether they like some Et'ada or not.
Hopefully I was able to clear things up for you, rather than confuse you more! :D
I (and others on the forum I'm sure) are more than happy to answer any more questions you have.
Weirdly, I was actually thinking about re-writing that sentence in the article because I also found it unclear. Do you think I should? Maybe change it to something along the lines of 'the distinction between Aedra and Daedra started to arise at this time' or something like that.