Sure! We're traumagenic ourselves, so we may not properly portray the experiences of other origins, and i suggest (/nf) asking some endogenic or other origins systems to clarify if we make a mistake! ^-^
Traumagenic: the most commonly known system origin in both medical spheres and online. This usually (but not always!) Refers to disordered systems with some sort of CDD (traumagenic systems are not always disordered though, just commonly are) who formed through intense trauma under the age of around 10.
Endogenic: mostly an umbrella term, used to describe systems who formed for some reason other than trauma. They may still have trauma, it was just not the cause of their plurality. This could widely vary, from spiritual reasons, psychosis/delusions, created systems or just. Being born like that. There are usually more specific sub terms used to describe why they formed, for example "willogenic". Endogenic systems are usually non disordered, but if they have gone through trauma, they may have a CDD (this is not me saying that you can have a CDD without trauma)
Mixed origins/traumaendo: these are two slightly different terms, with mixed origins being an umbrella term for any mixture of origins, while traumaendo specifically being a mixture of traumagenic and endogenic. This is basically, as it says in the name, a system forming for mixed reasons, not being able to specify one origin.
Willogenic/parogenic: these are again two slightly different terms, (parogenic is used by systems who specifically used tulpamancy, but willogenic refers to all created systems) but they both refer to systems that were created on purpose by the host/cores own will. This does not relate to radqueers or transids in most cases, and are generally non disordered. Willogenic/parogenic systems do NOT see plurality as a game, there are many valid reasons to create a system, for example to help deal with emotions (see internal families), or to process trauma by essentially manually doing what traumagenic brains do automatically. Plurality is not "easy" or fun for created systems as some anti endos would like to believe. Any other system origin may also have willogenic/parogenic headmates.
Quoigenic: quoigenic systems are essentially systems who do not know their origins, do not want to say, or don't think its appropriate to ask. A subset of this is praesigenic, which is specifically for systems who do not want to say their origins.
Spirigenic/metagenic: any system that formed for spiritual reasons, or has spiritual elements. This is not necessarily tied to any religion or practice.
Neurogenic: a system which formed by or in order to cope with a mental illness the body already had. This may be seen as a subset of traumagenic, but its up to the system to decide if they see it that way or not.
There are other system origins, these are the ones we're most familiar with/the most common ones. For other resources/a better understanding see: