Well, 'Killing for Love' being a true story implies that there are real - life events that inspired it. It might be about a person who becomes so consumed by their feelings of love for someone that they cross moral and legal boundaries. For example, they might kill a rival in love or someone they think is standing in the way of their relationship. It shows how love, when distorted, can lead to tragic outcomes.
The Killing is not based on a true story. It's a work of fiction that was crafted by the writers' imagination. However, it might draw inspiration from various elements and themes found in real-life crime dramas.