> only linked insofar as they both use prisons as "weapons", i.e, undesirable places to be in
They're linked in that "a sense of morality transcend[s] immediate self-interest and fear of punishment" [1]. Retribution links the justice system to our sense of morality. That deters crime.
The research on punitive damages tends to be more clear-headed than anything I've read on criminal law in this matter [2]. (For example, punitive damages provide "aggrieved parties with an attractive substitute for revenge.")