Answer
The prefixes di- and bi- both have to do with the number two. Sometimes the terms are used interchangeably to refer to systems that recognize two (primary) gods. Sometimes the gods are conceived of as two principles rather than personal deities. Both bi- and ditheism are forms of dualism, and sometimes bitheism or ditheism go by that name. However, we should note that there are also forms of dualism that do not include any deities. Some atheists are dualists who believe in a mind-body or matter-energy dualism with no deities involved.
When bitheism and ditheism are differentiated, ditheism usually refers to a form of dualism that teaches that the two primary gods are equal and opposing, one being good and the other being evil.
Bitheism recognizes two deities that are not in opposition to each other but rather complementary. In Hinduism, Shiva and Vishnu have opposite roles but are not antagonistic to each other. Both Vishnu and Shiva come from the supreme god Brahma, the creator, whose work is now finished. Vishnu is the sustainer of the universe, while Shiva is the destroyer. However, these roles are seen as complementary in bringing about change. Neither is opposed to the other, and in some literature they are even said to worship each other and help each other as necessary. (Shiva and Vishnu are the two primary gods of Hinduism, although Hinduism is properly labeled polytheistic, not bitheistic, since it has millions of gods.)
What is most important to remember is that the Bible does not teach bitheism or ditheism. Some people mistakenly conceive of God and Satan as being two equal, opposing forces, and in some cases, human beings as the deciding factor in the conflict. The Bible teaches that God is the Creator of all and there are no equals to Him. He is the Only God. “This is what the Lord says—Israel’s King and Redeemer, the Lord Almighty: I am the first and I am the last; apart from me there is no God. Who then is like me? . . . You are my witnesses. Is there any God besides me? No, there is no other Rock; I know not one” (Isaiah 44:6–8).
Satan is certainly opposed to God, but he lives under God’s authority. Satan cannot do anything without God’s oversight. For example, when Satan wanted to persecute Job, he had to gain God’s permission first. (See Job 1—2.) Satan’s freedom is limited in scope and duration. In the final judgment, he will be cast into the lake of fire (Revelation 20:10). For a time Satan opposes God, but, ultimately, even Satan’s opposition and rebellion are part of God’s plan and will result in His glory.