Hermetic Magic is basically method of magic that tries to marry science with magic, belief that there is a Universal Magical Theory that can be placed alongside other Laws of Physics. Emphasizes book learning and scientific method and is divided into various schools:
-Classic Hermeticism, belief in Ancients (the Greeks knew it all)
-Hermetic Druidism, leylines and stone circles enabled druid to draw magic from the land
-Teutonic Hermetics, Thule and Germanic beliefs
-Egyptian
-Qabbalah (magic comes from Yahweh, spirits are manifestations of his will)
-Christian (magic comes from God, spirits are manifestations of his will)
-Islamic (magic comes from Allah, spirits are manifestations of his will)
-Black/Satanic, not necessarily evil but combining scientific method with belief in the Adversary and quest for personal power
-Avant-Garde Thaumaturgy, magic as form of art
-Chaos Magic, magical theory based on Chaos theory and thinking that "magic" is a secret code that needs to be "hacked"
-Path of the Wheel, rigid Elven magical belief that life follows cycles, only available to elves from Tir na Nog or Tir Tairngire
-Wuxing (Ki and Celestial Bureaucracy)
-Buddhist (Tantric meditation, enlightenment)
-Hindu, karma and reincarnation, ascetism, mantras and yoga
-Wiccan, duality of nature so either Goddess Wicca or Gardner Wicca, belief in Gaia the Mother Earth,
Shamanic Magic is basically method of magic that accepts that magic is unknowable, organic, wild and only semi-controllable, stemming from life and/or the belief of sentient creatures and is divided into various groups:
-Classic Shamanism, animal totems (Fox, Bear, Wolf, Eagle, Owl, so on)
-Modern Shamanism, concept totems (Man, Dragonslayer, Seductress, Dark Lord, Trickster, so on)
-Norse (pick an Aesir to worship)
-Shinto, belief in Kami, finding harmony with them all instead of following one totem
-Aboriginal (Spiritwalking the Dreamtime)
-Aztec (Animal spirits, Aztec god, rituals and feathers)
-Voodoo, magic comes from spirit world and from the loa,
They are all correct and incorrect at the same time. The one thing that matters is that magic visualises itself differently to different people. So a Norse Shaman believes their power comes from Odin or Thor, allowing them to throw lightning bolts, whereas a Christian Hermetic believes their power comes from Jesus Christ, allowing them to throw holy bolts - but the mechanics and effects are the same. This is the same with spirits - an Egyptian Hermetic thinks they are summoning an avatar of Ra to assist them, while a Japanese Shaman thinks they are summoning a Kami of the River - but again the mechanics and effects are the same.
That should help you choose.