Interactive stories are player-created rooms that focus on telling a story by letting players explore multiple rooms; usually - but not necessarily - in a preset order. Common ways of telling the story include Holotars, Samplers, messages sent by chips, and writings on walls or sticky posters.
Adventure Games usually offer players more freedom to navigate the game world and tend to present more challenging gameplay.
Many rooms with interactive stories are tagged with #story. You can find them by searching for "#story" on rec.net.