What did the gods have in common?

What you call "stealing" is actually a very common phenomenon called "syncretism" -- when two or more civilizations meet they often alter their religions and other aspects of their societies as a result of the encounter. Similar things happened when Christians met Romans, Christians met Celts, Muslims met Hindus, Buddhists met practitioners of Chinese indigenous religions, etc.

They all have their origins in the proto-indo-european religion along with Norse mythology, Hinduism, and Zoroastrianism.