The evolution of human altruism toward strangers remains a puzzle. While a possible explanation may exist in the concept of punishment for non-cooperators, its own evolution depends on how others evaluate punishment. In general, punishment is assessed differently based on the context, with negative evaluations in the public goods game with punishment (PG-P), and positive evaluations in the third-party punishment game (TPP). This study examined whether different non-cooperation motivations could explain these inconsistencies; namely, the aim is to avoid exploitation (fear) in the PG-P, but to exploit the counterpart (greed) in the TPP. In turn, we posited that these motivational differences would respectively induce negative and positive responses to punishments for non-cooperation. To test this, we conducted a series of online experiments with hypothetical scenarios in which the motivations of non-cooperators were manipulated by the decision-making order. Two studies with a total of 842 participants consistently found inter-game differences regardless of the motivation for non-cooperation. Specifically, evaluations were more positive toward non-punishers (vs punishers) in the PG-P, but more positive toward punishers (vs non-punishers) in the TPP. In sum, these results highlight a general tendency to devaluate punishment as a way of maintaining group order.