This story is a crossover, but the systems are not automatically the same.
Soul Land has Martial Souls, Spirit Rings, Spirit Skills, Soul Beasts, Spirit Bones, spirit power, and Spirit Master ranks.
Fate/Nasuverse has Heroic Spirits, Servants, Noble Phantasms, Magecraft, Magic Circuits, Mystery, the Root, the Throne of Heroes, Alaya, Gaia, and the Counter Force.
These systems stay distinct unless the story directly creates a bridge between them.
Important separation rules:
A Spirit Ring is not a Noble Phantasm.
A Martial Soul is not Magecraft.
A Spirit Skill is not automatically a spell.
A Soul Land god is not automatically a Type-Moon Divine Spirit.
A Servant is not a Soul Beast.
Spirit Power is not mana unless the story directly equates them.
Magic Circuits are not spirit power.
Wu Ling's Martial Soul is special because it draws on Fate logic. That does not mean every Soul Land concept becomes a Fate concept. His power is a story-specific exception, not a universal system merger.
Fate terms kept in official English include:
Heroic Spirit
Servant
Master
Noble Phantasm
Command Spell
Reality Marble
Projection Magecraft
Reinforcement
Mind's Eye
Swallow Reversal
Throne of Heroes
Root
Counter Force
Alaya
Gaia
Sasaki Kojiro
Hassan-i-Sabbah
Angra Mainyu
The translation uses Swallow Reversal in narration when referring to the technique commonly known from Type-Moon, rather than leaving it as untranslated Japanese.