While I am thinking through my entire system how I am seeing it I think I can summarize it in touhou.


Higher magic. Reimu. She does everything via Shinto and the Gods

Lower Magic. Marisa. She collects elemental materials that she puts into her Master Spark cooks mushrooms writes her own Grimoire and the only reason she can operate because she lives in the "Forest of Magic" which is a magical forest that generates every ingredient for her craft. Mostly mushrooms. Without the ingredients Marisa would be a normal human and even ZUN stated that this is the reason why Marisa is the "Player's self insert character"

> It is representational magic, magic using words or symbolic artifacts or drawings, sigils
While higher magic can truly be influenced via using the ceremonial arts that is still a sort of "lower magic" that forces the "hand of higher magic" to do the bidding. 

> "lower magic". This has been called "cultivation"
True because you need to collect energy and burn clean the channels to reach the "higher truth" but lower magic refers to other ways too when you sacrifice things because with that sacrificed energy you can connect to entities "close" to earth dimension. For higher magic you need to transmute that energy in several ways. That is why that entire "ceremony" is needed.

> representational magic should not be practiced
That whole ritual is like dialing up a higher power and missdialing it might have dire consequences. I consider "higher magic" when you work with gods and with their energy/power but there are beings that are outside of our realm of existence that cannot be even categorized as anything. Accidentally summoning one that you are unable to handle is the dangerous thing. Theoretically it is impossible and only powerful and knowledgeable beings can do that. Theoretically... The chaotic nature of reality is not always that simple.


> place the different viewpoints on a map
Was thinking about drawing one but I need to gather my concepts and my confidence for that. As the image forms in my head my intuition is bothered how I am missing some points. This is too complicated and the way western and eastern traditions "meet" is not exactly makes things more easy to word.

> Higher magic should only be practiced by those called undead or immortal, or by prophets, diviners and others who channel information from higher beings
This is correct.
> When serving as a non-interfering device of a higher spirit, it is the higher spirit practicing magic, not the person him/herself.
While this is true there are ways you can internalize truth. That was the point of Bodhidharma. Awakened dharma of sorts. You are a higher spirit on earth but that is a long topic. And in the eastern traditions those who gained siddhis via spells or symbols or other lowly ways instead of having the truth internalized were looked down. That is not truth that is the emulation of truth which will result in desecrating truth because you will use it for your mundane ways/gains and that will "clog" the channels and cause anomalies. It's hard to save someone from hell when he creates an extremely special hell for himself that no one but the creator can access...
And yes lower magic is the mastery of elements be their inner or outer and gaining power via it. But breathing fire once you cultivate enough energy for a decade then getting an organ failure is not something useful again. That is why "proper instructions" are needed and a realization why you want these skills. Party tricks that have use only as an amusement but has no long term practical use is something every master discourages. Ceremonial magic can be used to target lower realms to but for that you need artifacts that were "blessed" via higher powers


This topic has more nuances ofc but I think this is enough for now