Dang...all my quotes disappeared and didn't make it to this post. I'll just summarize points I made.
1) In 5e magic officially draws upon an interface. This is a universal (multiversal?) rule, and is not campaign setting dependent. It doesn't matter whether you are in Forgotten Realms, Ravenloft, Dragonlance, Dark Sun, Eberron, whatever--you use this interface to channel the magical energy inherent in all things into spells and magical effects, according to the core rules. Spellcasters in the Forgotten Realms refer to it as "the Weave" and conceptualize it as relating to Mystra, but the same interface exists across the entire multiverse. Different settings have different ways of conceptualizing this same interface and may not refer to it as "the Weave," but it's the same thing.
Like it or lump it, that is the official stance of 5e. I need to put this in my sig with references or something.
2) The antimagic field spell explicitly blocks all magical effects, not just spells. This means it should apply to ki, as ki is referred to as magical in the description of the monk class under "The Magic of Ki."
3) There are apparently magical effects that make use of "the Weave" but are accessed by neither arcane nor divine means. The magic of ki is an example, and the specific magical nature of it (the energy that flows through living beings) is described in the monk class description.
The precedent of ki would imply there could be other types of magic, and that they would make use of "the Weave."
Moving on...
I think it could be useful to determine what magic is in order to determine whether psionics is/should be concepualized as magical.
In the real world, it's kind of hard to pin down what the concept of magic actually refers to, and definitions vary. Most people wouldn't consider "anything supernatural" to automatically be magical. For instance, parapsychologists aren't likely to call ESP or precognition magic, and most people aren't going to call the very existence of a ghost magical.
But that varies widely. For instance, many (perhaps even most) practitioners of magic consider things like ESP to be essentially magical. In fact, the impression that I get is that the more "into" magic a person or mindset is, the more broadly they are likely to define it--even going so far as to hit a point where they would consider everything to be magical--much like the way D&D explains magic as permeating everything. In the ancient world, the very concept of magic as an umbrella term may have been absent, since what moderns would term supernatural is a standard part of the world view and not a separate element that one can push certain aspects into. You might perform a ritual to create X effect, but there is no particular reason that is in a different category than performing a mechanical physical act to create Y effect.
Some religions consider portions of their supernatural practices to be explicitly magical. Other religions consider nothing they do to be magic-related, but would consider the religions of others to be magical. This is perhaps related to one view of magic whereby the distinction is made that magical practices involve procedures that are guaranteed to produce a result without the need for the approval of another entity (such as a god or spirit), while a religious miracle or sacred act only functions according the agency of such another being. From that view, if an entity assists you because you compelled it, that is magic. If you simply requested it to help and it chose to without compulsion that is religion--although some would say that the nature of the entity would also make a difference, regardless of its agency or lack thereof.
Some would make a distinction between magic and science by saying that magic is a violation of natural laws. But relatively few practitioners are going to agree with that. In fact, some practitioners of magic are more likely than others to believe that it simply functions according to natural laws as yet poorly understood, or technologically beyond the current ability of science to observe and measure, but theoretically fully possible of being brought into the umbrella of technology given sufficiently advanced tools. One definition along these lines might be to conceptualize magic as a technology of spiritual (interpreted very broadly) things.
Which brings us to an argument that magic is merely a term of ignorance. If we don't understand how it (would) work, it is magic. Magic equals superstitious mumbo jumbo. If something is understood it is by definition not magic. Again, that definition is very divorced from actual practitioners, as far as I understand it.
The clearest impression that I can get about the concept of magic, as viewed IRL (and it relates at least tangentially to my academic field), is that the more accepting or involved a person is with the concept, the more likely they are to view it in broad or expansive terms, and that the less accepting or involved a person is, the more likely they are to define it either narrowly, or as a term referring to superstitious mumbo jumbo in general.
So, with that background to clarify our own preconceptions, we can examine what the relationship between psionics and magic is in D&D.
As I mentioned early in the post, D&D defines magical energy as permeating everything, but being accessible only through "the Weave." Ki referred to as a type of magic, and there appears to be nothing in the text exempting it from Weave-access requirement.
We can see here that D&D is taking the position that:
A) Raw magic is omnipresent and all-permeating in an inaccessible format
B) All mortal magic is accessed via "the Weave"
From this point on I'm going to use "magic" to refer only to Weave-mediated effects, since position A essentially says "everything is magic" in a general sense, which isn't very useful for discussion
C) Mortal magic extends beyond spellcasting
However, there are certain things that we call supernatural which lack explicit magical connections and don't appear to have the sort of inherent connection to the Weave that would allow them to be affected by magic-dependent affects (such as detect magic or antimagic field). Examples would be supernatural beings themselves, such as celestials, fiends, fey, etc. They do, however, often make use of magical effects dependent on the Weave.
D) There are supernatural things that aren't magical (Weave-dependent)
We can also see that certain types of Innate Spellcasting seen in the Monster Manual are listed as psionic. This might imply that they are inherently magical, except that:
E) While it might be inferred, it is nowhere stated that all spellcasting accesses the Weave
Ironically enough, the rules therefore appear to support the possibility that psionics could involve non-magical spellcasting, or that spellcasting could draw on something other than the Weave, even though most people aren't really arguing for that sort of position at all.
So D&D takes a position that you have a general supernatural nature of the multiverse, which can manifest in certain things we would consider supernatural (such as fey), and that the "magic" that is dealt with by characters and creatures in the world is based on interaction with the Weave in one way or another (spellcasting is one way, ki is another).
This apparently allows for a couple of psionic models
Psionic Model #1) Psionics is a form of supernatural effect (ie, dependent on the raw magic that suffuses everything) that isn't dependent on the Weave, and is therefore considered "non-magical" in the same sense as a celestial isn't considered inherently magical.
Ramifications of this view include that psionics wouldn't be effected by spells like detect magic or antimagic field, but could affected by other possible spells like detect psionics or dispel psionic effect. Psionics could, however, still use spellcasting (though it doesn't need to, and probably wouldn't). This view, however, makes non-magical psionics contrast with the magic of ki. Since ki draws upon life energy, which is explicitly magical, it seems really odd to have an internal energy (of the mind, etc) that psionics draws upon not be magical. It would seem to have to draw upon something truly alien to justify this position.
Psionic Model #2) Psionics is magic, dependent upon the Weave like all mortal magic. This view drawing up ki as a precedent, allows psionics to be neither arcane nor divine, and to have the source of magic be accessed without spellcasting. Since the Weave is the means of accessing life-energy magic, it can also be a means to access the internal power of the mind/soul/etc, which could serve as the definition of psionics (though it could just as easily access any other type of magical energy from any source WotC chooses). Just as with other types of magic, it need not (and probably shouldn't) use spellcasting.
Because of the precedent of ki and the difficulty of explaining the source of psionics in model #1 without going sci-fi or Far Realm, I favor Psionic Model #2.
