Narrative opening is when the titles run through the opening as the film starts. For example, The Stepfather, Touch of Evil, Casino and The Taking of Pelham 123.
A discrete title sequence is a separately screened and conceived part. It is edited separately then the film starts rather than a narrative opening. An example of this is Seven where we have the view of the protagonist and the shots are either close ups or extreme close ups. The title has its own separate music to identify it as a separate piece. The character appears crazy as they are cutting they're skin with a razor and sowing material onto his thumb which suggests that he is abnormal.
Titles over a blank screen followed by the narrative opening. Its usually a dark screen with just sound effects which is very effective as it is mysterious and engages the audience into asking what is happening. An example of this is Donnie Darko where we have a view of dark mountains then unexpectedly somebody's head appears. This structure is very traditional.
One title sequence which inspired me is the split screen technique in Mezrine. It allows the audience to have different views and is fairly easy to do on final cut.