Personally I treat the Soul and the Spirit as distinct parts of the living entity.
The Soul is the animating life essence of a person, a unique living part of the Person that is seen as the aura and makes a persons unique nature. The soul is what dies (making the body go cold) and it can be stregnthened, dminished, consumed and even traded and used as an energy source by magical entities (usually demons who will make deals to possess them).
Everything that exists has a soul.
The Mortal Spirit is the Immortal part of a person that is anchored to the body in life and continues its ‘Being, Personality and Self’ even after death. Depending on religion a Spirit can go back to its Diety, become an Ancestral Spirit or hang around as a Ghost/Wraith/Spectre.
There are Spirits who are not Mortal Spirits and thus do not have bodies, some like Elementals and Djinn find their own anchors to the Material World, while some manifest from the concious existence of groups of things (eg Nations, Types of Animal, Beleifs). Spirits can be manipulated, summoned, enslaved and banished but generally can not be destroyed except in extreme circumstances.
A Body & Soul with no Spirit = Mindless Undead
A Body & Spirit with no Soul = Living Dead, Mummy, Vampire etc
A Soul+Spirit with no body = Ghost
Soul + Anchor = Haunt
Spirit + Anchor = Elemental, Wraith, Spirt