Comparative mythology observes that certain divine roles recur across unrelated pantheons. What recurs is not the same god under different names, a claim the evidence does not support, but similar offices filled by different figures in different traditions. The distinction matters, and the older habit of identifying deities across cultures, the interpretatio graeca and romana that made every foreign god a version of a Greek one, is now regarded as a source of confusion rather than of insight.
The sky father is a paternal deity of the sky and of authority. The Indo-European case is linguistically demonstrable rather than merely thematic: Vedic Dyaus Pita, Greek Zeus Pater, Roman Jupiter and Norse Tyr all descend from a reconstructed form meaning "sky father", and this is among the strongest single pieces of evidence for a common Indo-European religious inheritance.
The earth mother is correspondingly a deity of earth and fertility, Gaia, Prithvi, Papatuanuku, Pachamama, though the older assumption of a single universal prehistoric mother goddess is not supported by the evidence and has been extensively criticised.
The storm god wields thunder and rain and very often fights a serpent: Indra, Thor, Zeus, Baal, Perun, Tarhunna.
The sun deity may be male or female, and the variation is itself instructive: Ra, Surya, Helios and Sol are male, while Amaterasu and the Baltic Saule are female, a useful corrective to assumptions about which gender associations are natural rather than cultural.
The psychopomp conducts the dead: Hermes, Anubis, Charon, the Valkyries, Yama, the angel of death.
The chaos monster is the enemy of order, defeated at the beginning or held off continuously: Tiamat, Apep, Vritra, Leviathan, Jormungandr, Typhon.
The world serpent encircles or underlies the world: Jormungandr biting its own tail in the sea around Midgard, the ouroboros of Egyptian and later alchemical imagery, Shesha bearing Vishnu upon the waters.
Three explanations are offered for these recurrences, and they are not mutually exclusive. Common inheritance, demonstrable in the Indo-European cases through comparative linguistics. Diffusion and contact, demonstrable in the ancient Near East. And independent development from shared human circumstances, everyone has weather, a sun, and dead to dispose of. Where the evidence permits, specialists distinguish these; where it does not, the honest position is that a resemblance has been noticed and has not been explained.