This page is based on information presented in the cartoon, but is largely speculative in nature.
The core question that this page will attempt to address is very simple. What is "Magic" in Thundarr the Barbarian?
The answer is not simple. The short answer is: Magic is basically any source of energy that does not follow the known laws of physics.
A more precise definition is elusive due to the variety of sources of magical power seen in the show and the equally varied individuals who used them. Also confusing the issue is that there is no clear line between sources of power generated by advanced technology and magic, or even IF there IS a line seperating the two. While varied, the sources and wielders of magic can be placed into categories.
Sources of Power
Beings with innate power
The Abyss Wizard, Argoth, Ariel, Artemus, Circe, Dark Wizard, Merlik, Khromm, Mindok, Sarott, Sholow, Skullus, The Stalker from The Stars, and Striya each had powers that were apparently not derived from anything other than their own innate ability.
Cyborgs
Chom, Gemini, and Octagon had visible mechanical components of their bodies. Chom never used his powers in his brief appearance. Gemini's nature was unclear. He was obviously a cyborg, but his power source was apparently internal. Octagon relied on an external power source to augment his abilities, but had some power even without it.
Beings who use an external power source
Many people in the show use magical artifacts, however most of them are not identified as Magic users, exceptions to this include Infernus, Kublai, Valerie Storm, and Vashtarr. Each of them lost their powers when the source of their power was destroyed. The nature of the artifacts that granted their powers is unclear.
Titles
It's also worth examining the various titles used for Magic wielders.
Witch
Witch seems to be a pejorative term in the series. No character in the series ever referred to themself as a Witch. When someone referred to Ariel as a Witch, it made her angry and she loudly protested that she wasn't one. Circe was often referred to as a Witch by others, but never used the word to describe herself. At one point Circe indirectly described herself as a Sorceress.
What distinguishes Witches from other magic users? The only character identified as a Witch is Circe. Circe's specialties were turning people to stone, turning people to frog monsters, and the body swap spell she used on Ariel. Few, if any, other magic users had these abilities.
Also, Witch does appear to be a feminine term. It was only ever used to describe Ariel (who found it offensive) and Circe. Mazem and Striya, despite being female, were not referred to with the word Witch, but with either Wizard or Wizardess.
Sorceror/Sorceress
This term was mainly used in its feminine form to describe Ariel. It was used directly to describe Merlik. The interesting part is that Argoth indirectly referred to himself as a Sorceror when explaining that his powers would (like Ariel's) weaken if he entered the jungle near his citadel. Circe specifically said that she needed the body of a Sorceress to swap with. Thus hinting that she considered herself to be a Sorceress. Then in Portal Into Time, Khromm is twice indirectly referred to as a Sorceror.
What distinguishes a Sorceror/Sorceress from other magic users? The only thing that Argoth, Ariel, Circe, Khromm, and Merlik had in common was innate powers. None of them used magical artifacts as a power source. Argoth had a red gem that he used to control a monster, but this gem was apparently a tool only. Circe had a green orb she used in some of her spells, but it seemed to have no purpose beyond a magical conduit. But not all beings with innate magical power are referred to as Sorcerors/Sorceresses. Most are simply called Wizards.
Wizard/Wizardess
This term seems to apply to almost anyone experienced with wielding magic. The Abyss Wizard, Argoth, Artemus, Chom, Dark Wizard, Gemini/Janus, Infernus, Khromm, Kublai, Mazem, Mindok, Octagon, Sarott, Skorpos, Sholow, Skullus, Striya, and Vashtarr were all referred to as Wizards at least once. Yando is worth an honorable mention as he tried to become a Wizard by collecting powerful artifacts. Wizardess was only used once in reference to Striya.
What did they have in common? Not much, some were normal or normal-ish looking people who simply had magical powers. Others were freakish looking and almost monstrous. Mindok's body was nothing more than a living brain. Some were powered by magical artifacts, others had enormous reserves of innate power. The only evident commonality is Magic power. Argoth, Gemini, Mindok, and Vashtarr were among the most powerful Magic users ever seen in the show. Ariel was not powerful enough to defeat any of them in single combat. Chom, Dark Wizard, Mazem, and Skorpos were not seen using their powers. The rest were formidable opponents. Although Abyss Wizard, Skullus, and Striya were beaten in duels, they were not beaten easily.