Watch out — they’re trying to sell this movie as a thriller with supernatural overtones, but it turns out that it is a very traditional love story, and a surprisingly touching one, too.

Jennifer Lopez plays Sharon, a cop who is fearless on the streets but not ready to get close to anyone. As she tells one guy when he tries to get to know her over dinner, “I’m not very good at the whole dating thing,” She goes home to her apartment and lies on her bed in her bulletproof vest.

One day, just as an assailant is about to shoot Sharon, a mysterious stranger (Jim Caviezel) arrives to save her life. She is surprised to find herself drawn to him even though he tells her nothing about himself. All he will tell her is that his name is Catch.

Sharon investigates and interrogates people for a lving. She is not sure how much it is fair to expect to learn about someone in a relationship, so she does not push. In fact, it gives her some breathing room because she does not feel crowded by questions about her own past. She finds something freeing about a relationship between people who have only the present.

The connection between the two of them will be a mystery only to those people who have never seen a movie. But there is an appealing lightness and even a little wisdom the way their relationship unfolds. Sharon calls Catch and when he answers she tells him to hang up so that she can call his machine. She is not comfortable enough to talk to him directly, but at least she is able to tell him that.

Sharon and Catch both have to accept their pasts before they can face the future together. Although it is terrifying, they have to be honest with themselves before they can really be close to each other. Both blame themselves for family tragedies, and both have to accept that it is all right to go on from that. The movie has the great good sense to leave things a little messy.

Maybe Jennifer Lopez should stick with playing cops. This is her best performance since she played a marshall in “Out of Sight.” Caviezel, following roles in “Frequency” and “Pay it Forward,” seems to be the current go-to guy for playing “guys weird stuff happens to.” Screenwriter Gerald DePego and director Luis Mandoki show us the warm, easy connection between Sharon and Catch, and they make it clear that love alone is not the cure, just the motive to allow yourself to heal.

Parents should know that the movie is rated R for very strong language, brief non-explicit nudity and sexual references and situations. Characters are in peril and some are shot. There is a fatal automobile accident and a child is killed offscreen. Sharon jokes that she was looking for a man to “clean her pipes.” There are references to domestic abuse, and we see a woman who has been hit in the face.

Families who see this movie should talk about how we can find a way to create a balance between privacy and intimacy, between mourning a loss and moving on, between trying to make things better and accepting something less than perfect. They may also want to talk about Sharon’s conflicts over how to respond to her father’s abuse of her mother. When Sharon and Catch first become close, she asks him to kiss her somewhere she has never been kissed before — it may be worth discussing with teenagers the importance of keeping yourself precious enough so that you can give the person you love something that is just for the two of you.

Audiences who enjoy this movie will also enjoy some of the classic old romances like “I’ll be Seeing You” with Ginger Rogers and Joseph Cotten, “Love Letters” with Cotten and Jennifer Jones, and “One Way Passage” with William Powell and Kay Francis.