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In a recent question, an antonym for waning was requested. Waxing was naturally suggested, but the OP declined the word because he was actually looking for a word meaning non-waning, and thought that "antonym" was the word to describe his request.
The difference is: waxing means getting stronger/more intense and non-waning, if it were a word, would mean unchanging (not getting either stronger or weaker).
What is the difference between the words actually called, if not antonymous?
A few options here would be reciprocal:
Mathematics (of a quantity or function) related to another so that their product is one
This isn't quite as translatable into normal usage because the standard use of reciprocal means something more akin to equal or mutual.
Another option is reversal:
a change to an opposite direction, position, or course of action
While the opposite of wane is wax, the reversal of wane would be an un-wane. The subtle difference here is key:
The opposite of scoring a goal is not scoring a goal.
The reversal of scoring a goal is to take back the goal.
Hitting up a thesaurus then provides these alternatives:
And so on. Many words do not have appropriate reversals or antonyms and sometimes the same word can work for both.
In response to the edit, non- adds a third option to the pool which means "Not in the state of." This could be seen as an absence or negation. Much like how reversal and opposite can both apply, absence can fit into the same word as well:
This is hot; that is cold.
Hot is the opposite of cold; cold is also the absence of heat.
It's all to do with vagueness about the exact meaning of negation, opposite, etc. Necessary vagueness, because the world itself isn't black and white, so it's not always obvious how to apply 'disembodied' logic.
In the case of unwaning, as OP says, if it existed, the word would presumably mean not waning (i.e. – exactly the same as unwaxing, if we postulate such a word and sense).
The reason for this is simply that when we imagine the sense of unwaning we're likely to consider it within the context of a continuous oscillating activity, where negation invokes the idea of that activity not occurring at all.
The alternative, obviously, is to consider waning as one part of the two-phase process, giving waxing as the other.
This particular example covers just one of an almost infinite number of different ways things can be considered 'opposite'. Take loved, for example. Most people's first suggestion for an 'opposite' is probably 'hated'. It might take a while to realise that from a different standpoint, unloved is a more precise negation.
TL;DR: There are many different kinds of 'opposite'. The two in OP's example are perhaps the most common; reversal and absence (per @Hellion's comment, often indicated by un- and non-).
