Non-living
Non-living and unliving are terms that refer to creatures that have never been alive. The term non-living was introduced in the Shadow of Death manual, the only use of 'non-living' in the manuals (used to describe creatures unaffected by the Elixir of Life). 'Unliving' is not used at all in the manuals but replaces non-living in the in-game description of the Elixir of Life. The manual states that the artifact "does not work on Undead or non-living creatures". Additionally, the non-undead creatures not affected by the health bonus of the Elixir of Life, (golems, elementals and gargoyles), have other immunities in common, which allows them to be considered one group of 'non-living' creatures.
Stone and Obsidian Gargoyles are also considered non-living, but they are still affected by morale and mind spells.
Though war machines as units on the battlefield can be considered non-living in some sense, they have their own system of immunities.
Crystal Dragons, despite being "made entirely from red crystal and brought to life through magical means..." and being referred to as dragon golems in the campaign, they don't have any features that would set them apart from any other living creatures.
Non-living creatures
Golems
The only common trait of golems among all other non-living creatures is spell damage resistance.
Elementals
Air and Storm Elementals
Water and Ice Elementals
Fire and Energy Elementals
Earth and Magma Elementals
Psychic and Magic Elementals
Gargoyles
Immunities
All non-living creatures are unaffected by the 25% health bonus of the Elixir of Life, by morale (except for gargoyles), and the following spells and abilities:
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Archangels' resurrection ability
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Mind spells (except for gargoyles)
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Unicorns' blinding ability
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Fangarms' hypnotize ability
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Creature abilities
Azure Dragon: fear
Ghost Dragon: aging
Lich and Power Lich: death cloud
Mighty Gorgon: death Stare
Pit Lord: summon demons
Vampire Lord: life drain
Wyvern Monarch: poison
Sea Serpents and Haspids' poison
Zombie: disease