It has something to do with when and whence the words came to English. It seems that aureole is via Middle English from Latin (short for corona aureola 'golden crown'), but aureola is directly from Latin aureolus, -a, -um 'golden; splendid' from aureus, -a, -um 'golden'. And let's not forget oriole, the passerine bird, via the French.

And, addressing the original question, which I ignored earlier: English areola is from Latin areola diminutive of area 'open space; park; threshing floor'. So, the two words are not really related.

Ceci n'est pas un seing.