First of all, I want to start by saying that as a psychologist I love when people correct me about things I've studied extensively. No better feeling.

That said. Yes, pareidolia and apophenia are related phenomena. However, the term apophenia is almost exclusively used in a psychiatric context (less so by economists and staticians). So, yes, Wikipedia can be and is often wrong. In this particular instance I can notice that the affirmation “Pareidolia is a type of apophenia involving the perception of images or sounds in random stimuli.” or “Pareidolia is a specific but common type of apophenia” as it appears today in the English article (only article to affirm such, it is not present in French, Spanish puts the affirmation into question with a 'citation needed', most other languages are stubs who link the articles together but without the affirmation) for apophenia, lacks any sort of source. They are related and we suspect they might come from the same underlying neural mechanisms, but they are distinctly different phenomena. To call one a type of the other is an epistemological error without any proper academic source to back it up.

I am, however, sure that in the context of internet discussions, my expertise is about as good as the perception of anyone who just learned about the word a few days ago.

Coincidentally, to believe adamantly, against any evidence or factual authority that pareidolia is apophenia might actually be classified as apophenia…

EDIT: Just noticed that one of the sources used by the wikipedia article quotes the wikipedia article to claim that apophenia is audio pareidolia. Ultimate circularity achieved. If the source is “Wikipedia said so”, you've lost the plot.