In May 2019 I was asked what geographical feature orography was the study of. This was a new word to me; but of course, the answer had to be "mountains".
So what, if anything, is the difference between orology and orography?
Etymologically, I would suggest that orology is the scientific study of mountains, while orography is writing about mountains.
I checked with dictionary.com, and was surprised to find that it didn't recognise 'orology' as a word. It redirected me to 'orography', which it defines as "the branch of physical geography dealing with mountains." (This means that dictionary.com recoginses 'orology' as a word that people use, but doesn't think it's a proper word.)
I also checked a couple of printed dictionaries. The New Oxford Dictionary of English (2001 reissue) recognises 'orogenesis', but (surprisingly) neither 'orology' nor 'orography'; but Chambers (13th Edition, 2014) has all three. Chambers defines 'orology' as "the scientific study of mountains", and 'orography' as "the description of mountains". Which is pretty much what I said in the first place.
Dictionary.com's definition is the only one that points out that orography is a branch of geography; and it's interesting to compare 'orography/orology' with 'geography/geology'. Chambers defines 'geography' as "the science of the surface of the earth and its inhabitants", and 'geology' as "the science relating to the history, development and structure of the earth's crust". In other words, geography and geology are both sciences, but distinct from each other; whereas the difference between orography and orology, I would suggest, is much more blurred.
At the end of the day, I don't think you could blame the question setter for implying that orography is a science – especially as dictionary.com says it's a branch of geography.
© Haydn Thompson 2020