Theistic Satanism
Theistic Satanism is an umbrella term for a group of different religions centered on the belief in and worship of Satanael. This category may be termed the Satanic religions, to follow the naming convention of other religious categories (e.g., Dharmic religions).
Definition
A religion belongs to the category of Satanic religions if it:
Some Satanic religions use other names for Satanael; in fact, the only one that primarily uses the name Satanael is Satano-Grigorism. The majority of Satanic religions use the names "Satan" and/or "Lucifer" for their god, although these names are less than ideal (see the names to avoid section of Satanael's article.) Using a different name does not disqualify them from requirement #1 above.
Some Satanic religions also use a different definition of worship than the one employed by the Grigorist Temple of Satanael (which is the one used across Grigoripedia). Because of this, some Satanists will claim they do not worship Satanael; they may say they "revere" or "work with" him. However, if they are praying to him, praising him, meditating with him, or offering to him, they are still Satanists — what they do counts as worship according to the definition used in requirement #2.
Labels
Some Satanists identify themselves using other labels, such as "Diabolist" or "Luciferian." These are still forms of Satanism as defined above.
Types
There are many different Satanic religions. Classifying them can be very difficult for various reasons, the largest one being that many independent Satanists maintain an idiosyncratic religion whose specific beliefs may be held only by them. However, rough categories can be established based on the contents and origin of their beliefs.