Patrol areas are where the units stay. You put up a patrol area and no other units, and the patrolling units will just go in that area, it doesn't matter if "Investigate contacts outside" is turned on or if there's a prosecution area.
Without prosecution areas, switching "investigate contacts outside" is huge. If it's off, they won't investigate anything outside of the direct patrol area. If it's on, then they'll run off and investigate everything. To put it in a cynical manner, either your carrier CAP ignores the enemy launching a standoff attack because they were outside the patrol area, or they neglect the same enemy because they were too busy making sure that the little Beech flying a good distance away was in fact a little Beech.
But with prosecution areas, you can have the CAP stay fairly close to the carriers-but still rush for the unidentified contact closing a greater distance away, while ignoring what should be ignored.