Having analysed multilple different thriller film openings i have noticed that there are three basic structures.
For instance we have, Narrative film openings with titles this is where in some films the narrative starts immediately usually introducing the location, setting and lastly characters to the audience sometimes consisting of titles running throughout the whole opening sequence.
Titles over a blank screen, this is when a movie starts with a blank background/screen and rolling titles with either sound effects or sound track playing throughout later introducing us to a character, location or a object.
Finally theres Discrete title sequence openings.
Enemy of state
This is a perfect example of a discrete title sequence opening. Throughout the opening scene you notice that there are very heavy editing and stylised and comes across very technological due to the use of colour, sound, switching between clips and the overall use of editing also the use of font some of which make the letters look like symbols.
It tells a story or a plot but stands completely apart from the opening of the actual film.