I am not sure the examples, on the page and in the separate pages really always show "aji" as opposed to "nerai" examples. I am pretty sure the third example on the page will be commented with nerai / nerau family words in Japanese. This is not related to the WME and a problem with the confusion over both in most of our minds I guess.
I would like to see aji examples from Japanese commentary here. As opposed to fellow deshi's somewhat vague notion of aji as understood in the west.
See also: NeraiExamples, Nerai/Discussion (features exactly the same diagram as the 3rd on the aji page as an example of nerai)
The way I would differentiate the two terms myself is that aji refers to the existence of the weakness, while nerai refers to the act of aiming at the weakness for possible exploitation later. In other words, they're two sides of the same coin. In the 4-4 point joseki example, I would differentiate the two terms as such: