As seen in The Stepfather, a narrative opening is an opening that has titles running throughout it. This was also illustrated in my favorite title sequence Grand Theft Auto 4.
A Discrete title sequence
As seen in the opening of Seven. A discrete opening is a title sequence that is heavy on editing and very graphic, proven well by seven because the title sequence is of a man shaving skin from his fingers. Very enticing to a stereotypical psychological thriller audience as it ticks many characteristics they serve.
Titles over a blank screen
Bluntly as the title states this opening sequence from the movie Donnie Darko puts its title over a blank screen. Putting far more viewer concentration on the makers than the other thriller openings. These openings are usually immediate, at the beginning of the movie. They also commence more subtle and care free.
The fourth and final structure of a thriller opening is stylized editing. Very unique, stylized openings seem very much like the ending of a film as the credits accompany clips from the film as shown in the film Mezrine.