What exactly are the differences between the table triggers "WRITE" trigger and "REPLICATION-WRITE" trigger ??
Usually WRITE triggers are used by the "owner" of the application if write triggers are necessary. REPLICATION-* triggers are then left available for non-application owners to do something when the particular event occurs.
A typical example is when someone buys an application without the source code, but wants to hook into these events. Without the REPLICATION-* triggers, the TRIGGER source code would need to be changed.
You should be very careful to not change the application behaviour in the REPLICATION-* triggers (ie. no RETURN NO-APPLY or unhandled errors).