We study two generic versions of public goods problems: in Provision problems, the public good does not exist initially and needs to be provided; in Maintenance problems, the public good already exists and needs to be maintained. In five lab and online experiments (n=2,584), we document a robust asymmetry in preferences and perceptions in two incentive-equivalent versions of these public good problems. We find fewer conditional cooperators and more free riders in Maintenance than Provision, a difference that is replicable, stable, and reflected in perceptions of kindness. Incentivized control questions administered before gameplay reveal dilemma-specific misperceptions but controlling for them neither eliminates game-dependent conditional cooperation, nor differences in perceived kindness of others' cooperation. Thus, even when sharing the same game form, Maintenance and Provision are different social dilemmas that require separate behavioral analyses. Despite some inconsistencies, a theory of revealed altruism comes closest to explaining our results.