It might help to consider that, on the one hand, cleanliness is derived from the dated adjective cleanly, which means
(of a person or animal) habitually clean and careful to avoid dirt.
— Oxford Dictionaries
On the other hand, cleanness is derived from the adjective clean, which has the following basic meanings:
- free from dirt, marks, or stains:
- morally uncontaminated; pure; innocent:
- free from irregularities; having a smooth edge or surface:
— Oxford Dictionaries (Visit for elaboration on various meanings and usage)
The word cleanness can thus be used in any of the senses of the word, clean, in reference to people, places, things (inanimate and abstract e.g. buildings, sounds, etc.), actions, and so forth. Also, note that cleanliness can only be used for people or animals.