We Aren't Here For Revenge

Alex had known from the start that his time with Claire was limited. Originally he hadn't cared; all he wanted then was to satisfy his curiosity and get back to what he was familiar with.

Along the way that had changed. She became the most important thing in the world to him. The one person he actually cared about. She was an irreplaceable existence now and he wanted to spend as much time with her as he could.

Claire's house felt more like home to him than headquarters ever had. He had known both words but thought they were interchangeable before meeting her, looking up the difference between the two later when he became more interested in definitions of words.

A house referred to a building where someone lived. A home could refer to that or any place that a person thought of as belonging to them. The latter had a more emotional connotation.