Here are the definitions of the various Theisms and related technical terms as I understand them, with links to Dictionary.com for comparison, when available. Some of these refer to specific movements historically (or at least, they started there), whereas others refer to more general concepts that occur throughout the world. Some of them may be also used as identity labels. The definitions as I give them below describe the concepts themselves, rather than describing people, or experiences.
Note: As this is a reference post, I am editing this over time to add more terms as I see the need, and sometimes to add a bit more to a definition, as I realize something was left out. I will NOT, however, substantially change the definitions given here without leaving some note as to what was previously said. I don’t anticipate major changes in my understanding of these words anyway, to be honest.
Theism – Belief in divinity, i.e. God[s].
Deism – a Rationalist belief in divinity exclusive of the supernatural. i.e. God as First Cause, that which prompted the Big Bang and defined the natural laws of the Universe, but does not intervene outside of those laws.
Atheism – Not believing in divinity, or, more strenuously, a belief that there is no divinity. Classical/Archaic usage refers to a person who, in a context that takes the existence of the gods as a given, nevertheless refuses to acknowledge, honor, or interact with Them.
Nontheistic – Not involving belief in divinity one way or the other. e.g. Zen Buddhism does not require, but does not preclude, belief in divinity in any way.
Agnosticism – Not knowing if divinity exists or not, or, more strenuously, believing it’s not possible to know.
Monotheism – Belief that divinity is singular, i.e. there is only one God.
Duotheism – Belief that divinity is dual, i.e. there are precisely two Gods. The only example I know of this is the Wiccan Goddess & God, which is not always in a context where those two gods are the only gods there are. Sometimes it’s in the form of All Gods Are One God and All Goddesses Are One Goddess, sometimes it’s that there are these two gods that go together, and countless others elsewhere. The latter is a form of Henotheism (see below).
Trinitarianism – The Christian belief that divinity is singular, but experienced in three distinct forms – the Godhead “Father”, which is the abstraction usually thought of as “God”, the manifest “Son”, Jesus, who spent a lifetime as a human person, and the indwelling “Holy Spirit”, which resides within each person. Sometimes construed as a form of polytheism, while emphatically defined as a form of monotheism by its adherents. Whether it qualifies as such depends tremendously on how concretely one interprets the word “Polytheism”. [Edit] There’s also the Hindu Trimurti, but that’s not quite the same concept as the Christian Trinity, and what exactly it represents depends on which Hindu tradition is involved. Attempts to equate the two are common, and usually erasive, in that they’re often born of a historical insistence that religions are only legitimate to the degree that they resemble Christianity.
Polytheism – Belief that divinity is plural, i.e. there are many Gods. This can be a belief in one specific pantheon, or a more general belief that all the gods of various cultures exist. Examples of both abound throughout history.
Omnitheism – A new-to-me term that seems to indicate belief that all gods are real in a polytheistic context, and holding respect for, if not actively seeking relationships with, all gods. (Apparently coined, at least this time, by Anomalous Thracian, but I haven’t been able to find the relevant post yet, sorry.)
Unitarianism – Belief that all gods are one god. Originally in contrast to Trinitarianism, rather than Polytheism. When paired with Universalism, used to emphasize that all depictions and experiences of divinity are equally valid, within a Monotheistic context.
Monism – Belief that All Is One, i.e. that everything that exists is part of a unified Whole. That whole may or may not be conscious, and may or may not be understood as divine. That whole does include the gods, if any are described. That whole does not necessarily unify a plurality of gods into one God before it unifies all of existence. Monism as we know it is usually pulled from certain Hindu beliefs which assert that everything is part of the Divine Whole, not just the various depicted gods.
Pantheism – Belief that All is Divine, i.e. that everything that exists is part of a unified whole, and that Whole is God. More simply put, The Universe Is God. Originally in contrast with the doctrine of a Monotheistic Divine Creator separate from Creation. In practice, Monism and Pantheism are usually the same today, although they started in different ways. Monism can be non-theistic, and Pantheism can be rationalistic. Connotatively, “Monism” is often used to emphasize the Oneness, whereas “Pantheism” is used to emphasize that all things are parts of God.
Panentheism – Belief that divinity is WITHIN all things. This is subtly different from Pantheism in that it is not describing a oneness of existence, but rather, that an essence of divinity dwells within all things separately. This is orthogonal to, and thus compatible with any number of gods. [ETA] Basically, a belief that divinity is immanent. As noted in comments below, this is not necessarily instead of divinity being transcendent. Christian theology consistently describes God as being both.
Animism – Belief that spirit, soul, and/or consciousness is a trait of all things, or at least all living things. This is not the same as Panentheism, in that Animism attributes both some level of consciousness, and some level of autonomy to things, whereas Panentheism attributes that indwelling spirit to a more general source.
Henotheism – Loyalty to a singular deity in a polytheistic context. “This is my God. There are other Gods, but this one is mine.” Common in the Ancient world, as many places or tribes had a local deity who was the patron of that group, to whom everyone in or from that group would direct all petitions, understanding that other locations and tribes had other patron deities. The Abrahamic tradition was Henotheistic before becoming Monotheistic, and it shows in the older scriptures, like the First Commandment.
Syncretism – The practice of correlating deities from other cultures to the deities of a particular culture (usually one’s own), and thus accessing one deity through the representations of another deity. Romans did this a lot, equating, for example, Thor with Zeus, and referring to their conquered countries’ gods as epithets of their own gods, e.g. Mercury-Hermes. Afro-Diasporic traditions did this out of the need to hide their traditions behind the veil of accepted Christian symbols, usually Roman Catholic, thus correlating all their traditional powers with Saints, Angels, Prophets, etc. Hence Ochun represented by Nuestra Señora de la Caridad del Cobre, in Cuba. Over time, the correlation is so strong, the names are treated as totally interchangeable, e.g. San Lazaro IS Babablu Aye, and even non-Catholic practitioners of La Regla de Ocha may call Him that.
Orthodoxy – “Right Belief”, i.e. having the correct thoughts and beliefs accepted by a particular doctrine or group. Christianity in general is well known for being an Orthodoxic tradition, focusing on the nature of faith itself, and making sure that the correct beliefs are accepted and taught within any given denomination.
Orthopraxy – “Right Deed”, i.e. having the correct behaviors and practices accepted by a particular doctrine or group. Many indigenous traditions are Orthopraxic, focusing much more on the forms of respect than one what beliefs an individual may have behind them.
Orthopraxy and Orthodoxy are not in opposition to each other. Indeed, Dictionary.com treats them as nearly synonyms, and many traditions require both. In Religious Studies, however, they are understood to indicate different priorities. Most traditions placed one higher in priority than the other, and that can have a profound effect on the resulting group culture.
A side note:
Hard vs. Soft – How concrete vs. abstract, or otherwise how permeable the category definitions are, with respect to a particular belief above. I have heard this used only in three examples:
1: A Soft Atheist does not happen to believe in divinity, but their lack of belief does not address the nature of divinity. A Hard Atheist firmly beliefs that divinity does not exist, and that this nonexistence is a trait of divinity itself.
2: A Soft Agnostic does not know if divinity actually exists, but their lack of certainty does not address the nature of divinity. A Hard Agnostic firmly beliefs that it is not possible to know if divinity actually exists, and that this unknowability is a trait of divinity itself.
3: A Soft Polytheist believes divinity may manifest as multiple, but this multiplicity of experience does not address the nature of divinity. A Hard Polytheist firmly believes divinity is multiple, and that this multiplicity is a trait of divinity in itself.
By this standard, I am a Hard Polytheist, and I’m fine with that. I have heard an argument (from PSVL, but others may have similar arguments) that “Hard” vs. “Soft” has sexist connotations, and thus using them in this context is sexist. I do understand that our culture attributes hardness to masculinity and softness to femininity, and if that were the basis for this comparison, I would reject it too. However, I do not believe that is the source of this usage, and do not think that all usage of “hard” and “soft” as adjectives should be rejected just because they are inappropriately correlated to gender in other areas, so in this case, I respectfully disagree with PSVL’s analysis.
There’s also an entire conversation I need to re-post here about the difference between Polytheism and Monotheism w/ non-God Spirits, explaining why the Orixa, Lwa, etc., are not considered Gods in Afro-Diasporic traditions. [Edit] Here it is!