The Greeks, philosophers, regarded the gods as rather dangerous, unpredictable, sometimes-quixotic and sometimes-malicious forces that could upend human lives on a whim. They sacrificed and worshiped in a spirit of propitiation and/or prophylaxis, to hopefully invite helpful divine interventions and/or ward off the most childishly malicious actions - but they always acknowledged it was essentially a crapshoot, as the gods would do what the gods would do for their own divine reasons. They allowed the gods a role in delivering retribution for human evil, folly, etc., but also acknowledged the inherent unreliability of divine justice.
Romans, jurists, ascribed logical, transactional motivations to their gods. They believed the gods had, essentially, a contract with Rome, and as long as Rome did her part in carrying out divine instructions (as revealed by aediles and priests) the gods would deliver victory, prosperity, etc. Even the minor household gods operated on this transactional model. Sacrifice to the Lares, and your children would make worthy marriages, your name be respected, etc. Propitiate the Penates, and your supply of olive oil would never run low. If something did go wrong, it wasn't the capriciousness of the gods but some failing on your part or just possibly the intervention of an unpropitiated god with superior powers.
Even in the developments of early Christianity it is possible to trace the differing influences of Hellenistic thought versus Roman practice, culminating in Constantine's deal with Sylvester I and the Council of Nicaea.
interestedly,
Bright