(paraphrased from Wikipedia)
Types of polytheism:
Polytheists do not always worship all the gods equally, but can be Henotheists, specializing in the worship of one particular deity. Other polytheists can be Kathenotheists, worshipping different deities at different times.
Hard Polytheists believe that gods are distinct, separate real divine beings - not
psychological archetypes or personifications of natural forces. Hard polytheists
reject the idea that "all gods are one God". It is a misconception that Hard Polytheists consider the gods of all cultures as being equally real; that is a theological position more correctly called
integrational polytheism or omnitheism.
Reconstructionists - those who are reviving a religious practice from an ancient culture, such as Egypt or Greece - are usually hard polytheists.
This is contrasted with Soft Polytheism, which holds that Gods may be aspects of
only one God, psychological archetypes, or personifications of natural forces.
Soft Polytheism is prevalent in New Age and syncretic currents of Neopaganism,
as are psychological interpretations of deities as archetypes of the human
psyche. English occultist Dion Fortune was a major populiser of soft polytheism.
In her novel, The Sea Priestess, she wrote, "All gods are one god, and all
goddesses are one goddess, and there is one initiator." This phrase is very
popular among some Neopagans (notably, Wiccans) and incorrectly often believed
to be just a recent work of fiction. However, Fortune indeed quoted from an
ancient source, the Latin novel The Golden Ass of Apuleius. Fortune's soft
polytheist compromise between monotheism and polytheism has been described as
"pantheism" (Greek: pan 'all' and theos 'god').
However, "Pantheism" has a longer history of usage to refer
to a view of an all-encompassing immanent divine.
Neopaganism often blends polytheism with pantheism or panentheism.
Types of monotheism:
Monotheism is the belief in a Singular God, in contrast to polytheism, the belief in several deities. Polytheism is, however, reconcilable with inclusive monotheism or other forms of monism and the distinction between monotheism and polytheism isn't clear-cut or objective.
Henotheism involves devotion to a single god while accepting the existence of other gods. Though similar, it contrasts drastically with monotheism, the worship of a single deity independent of the ontological claims regarding that deity.
Monotheism is often contrasted with theistic dualism (ditheism). However, in dualistic theologies such as that of Gnosticism, the two deities are not of equal rank, and the role of the Gnostic demiurge is closer to that of Satan in Christian theology than a diarch on equal terms with God (who is represented in pantheistic fashion, as Pleroma).
Monotheism can involve a variety of conceptions of God:
Deism posits the existence of a single god, the Designer of the designs in Nature. Some Deists believe in an impersonal god that does not intervene in the world, while other Deists believe in intervention through Providence.
Monism is the type of monotheism found in Hinduism, encompassing pantheism and panentheism, and at the same time the concept of a personal god.
Pantheism holds that the universe itself is God. The existence of a transcendent being extraneous to nature is denied.
Panentheism is a form of monistic monotheism which holds that God is all of existence, containing, but not identical to, the Universe. The one God is omnipotent and all-pervading, the universe is part of God, and God is both immanent and transcendent.
Substance monotheism, found in some indigenous African religions, holds that the many gods are different forms of a single underlying substance.
Trinitarian monotheism is the Christian doctrine of belief in one God who is three distinct persons; God the Father, God the Son and God the Holy Spirit.