As far as I understand, saying that two words are polysemes is saying they're synonymous homonyms, but not synonymous enough to be the same word. Senses on the other hand, are synonymous enough to be counted as variations of the same word.
Perhaps it is not the degree of synonymy that is the distinguisher, but rather the nature of the synonymy? Perhaps senses are variations of a word's definition depending on context, whereas polysemes arise from the metaphorical usage of words?
So, murder can mean "partaking in any action leading to the death of an organism" in common parlance (one context), and mean "intentionally make a person die" in legalese (another context). One is in fact a generalization of the other (if that's important).
Whereas pig can mean the animal pig, or it can mean person that acts in a disgusting way; one is in no way the other, but has arisen from analogy and symbolism.