As noted in a comment, synonym and antonym are fairly elementary concepts for lexical semantics - there's quite a bit more. There's hypernym and hyponym, meronym and holonym, there's opposite and negation and counterpart and entailment. It all comes down to semantic relations.
The most general term for this is simply 'related concept'. This is very broad (it includes the 'is-a' and 'has-a' relations). While both those relations allow some synonym-like activity (eg maintaining most meaning when replaced), antonyms and opposites usually relate terms on the same level.
Some concepts have more than one other related concept on equal footing. So 'red' usually isn't considered to have a single opposite, because there's yellow and blue and green and none stand out as an opposite.
Some concepts have just one concept and here the general term is 'counterpart' (though this is not a technical term). For example, wet and dry are counterparts but so are lock and key though the latter are in no way considered antonyms. Another term for such counterparts in general is 'complement'.
Often these counterparts come on a continuum so that 'wet' and 'dry' are on opposite ends but then 'moist' and 'arid' and 'drenched' fall on the scale.
The term 'complement' is sometimes used more specifically as 'negation'. That is, the complement of 'dry' is everything -but- dry, including only the slightest bit of moisture. Which is to say 'not dry' and this is not the same as 'wet' (though 'not dry' certainly include 'wet').
For pairs in opposition (are these called 'opposites'?), there are many possible dimensions and many possibly ways and frankly these can be constructed artificially or by new means. Remember the 'red' example? Some might say that 'red' is on the opposite side from 'green' on one type of color wheel.
If one thinks of words having a meaning described by a collection of binary (or continuous) 'semantic features', then one can then compare two words to see how 'opposite' they are.
Take 'besiege' and 'occupy'. Both have the semantic feature of 'kind of military situation'. Also, they both are somewhat 'static' (a siege just sits there, similarly an occupation. But you could say that to besiege is to 'surround a place and stop things going in and out' and 'occupy' is to 'invade (or be in) a space and let things continue' (yes this is arguable). But with these features, the contrast is not negative or on the other end of a scale but more like key and hole. I would label the relation between these two as a complement. Or to fill in the blank (or really reword appropriately):
“'To occupy' and 'to besiege' are complements of each other”