There are some similarities. First and most important is the presence of the narrator. It is his voice rather than his identity that is significant. He is established in the introduction as a man of imagination and curiosity, and these traits are reflected in the way he tells the the story. As he relates it, his information having been gleaned from old documents and old tales, his voice is often ambiguous and filled with qualifications as he offers up one possible version of events versus another. He asks many questions. His curiosity inspires curiosity in the reader. The truth of the events he relates is as much a mystery to him as to the reader.
There are also some similarities between the narrator and, strangely enough, Hester Prynne. Both live in circumstances where they really do not belong. The narrator is at heart a writer, trapped in the mundane life of the Custom House and surrounded by people far different from himself in their values, behavior, and temperament. He goes about his business, performing his duties, but he does so without really belonging. He is an outsider who observes those around him while remaining essentially detached. It is understandable why he would be drawn to Hester, intrigued by a woman who lived and died in her own difficult circumstances among people so unlike herself. Like Hester, the narrator is emotional, passionate, and nonjudgmental, very much aware of the unresolved mysteries in life.