Are you familiar with the disparity, in Platonic thought, between manifested things and perfect forms? If so, you get the gist of the disparity between Adam and Adam Kadmon.
Adam Kadmon is the perfect/complete form of Adam, which form dwells within the Sephiroth. Adam Belial, known also as Edom Belial is the Qliphothic equivalent of Adam Kadmon. That is to say, it/he is the manifestation of Antinomian/Adversarial perfection whom Liber HVHI describes as “the will made flesh.”
Adam Belial, often confused with Belial, is attributed to the Qliphothic spheres of Ghagiel (Uranus/Baelzebuth) and Sathariel (Saturn/Lucifugus Rofocalus), being the penultimate realms of the Qliphoth’s outer two pillars (the Pillar of the Nurturers and the Pillar of the Destroyers), standing at the Right and Left of Da’ath as the Saturnian-Uranian human ideal.
Above: Original Sigil of Adam Belial
Adam Belial means “Adam the Wicked.” The English word wicked connotes the Adversarial/Antinomian ethos and descends from the same root word as Wicca (witch), hence the English titles “Lilith the Wicked” and “Samael the Wicked.”
His correspondences through Gematria are as follows.
118: Zimimay (North/Earth); Bosom/Hollow/Midst; To Pass On/To Pass Through; To Be Hoarded/To Take Possession Of; Royal Power/Strength; Wealth/Treasure/Riches; Spring of Water; Aziel; Uzziel; Music/Song/Taunting Song; Stream/Division/River; To Cleave/To Slice; To Be Cut Off/To Break/To Snap
678: As He Fed; And You Shall Put Away/And You Shall Exterminate; And Burned; And Was Famished; And Passed Over; Their Chariots; You Shall Kindle; You Shall Go/You Shall Pass On; You Shall Pass Over;
The chant used to call him forward is “Liftoach Pandemonium, et germinet Adam Belial” [Open the Infernal Plane, and Bring Forth Adam Belial] and Io Edom Belial [Hail Edom Belial].