Re-Route is used for events in the PAST.   They have one date-time field that can be edited with a past date/time and they go on the trip as a completed event.
Check Call is used for events in the PRESENT.  These will auto-populate the current date/time and go on the trip as a completed event.  Not to mention the satellite integration.
Deadhead is used for events in the FUTURE.  These allow for an arrival and departure time when they get completed and have a field for SCHEDULED time. For example: 


If a driver is headed to a tire center and is SCHEDULED to be there in 30 minutes, then a Deadhead is the most obvious choice.  When he arrives and departs the times can be updated accordingly.  (Note: This can also be accomplished with Automated Workflow)  They must remember the difference between SCHEDULED and ACTUAL.  It is impossible to report an ACTUAL date/time in the future.  That - by definition- is SCHEDULED.