Both species benefit. Classic examples: mycorrhizal fungi ↔ plant roots (fungus gets sugar, plant gets minerals); clownfish ↔ anemone; fig trees ↔ fig wasps. Obligate mutualists cannot survive without each other.
The parasite benefits at the host's expense. Intimate parasites may coevolve toward reduced virulence (host survival benefits parasite transmission) — though highly transmissible pathogens can remain highly virulent.
Coevolution is modeled by modified LV equations with interaction terms. Mutualism creates runaway positive feedback (bounded by carrying capacity); parasitism creates predator-prey-like cycles.
Host-parasite coevolution drives continuous arms races: hosts evolve resistance, parasites evolve counter-resistance. This Red Queen dynamic may explain why sexual reproduction (generating diversity) is maintained despite its costs.