As for the difference between 'Whole' and 'Full' backup here is what the manual (Database Administration (Oracle) with SAPDBA) says:

Definitions
Complete backup is a generic term. A complete backup can be one of the following:
1. A whole backup -m all:
Backs up all database objects. This backup is not cataloged which means that you cannot
use this backup as a reference backup for an incremental backup with RMAN.
Syntax: backup_mode = all
2. A full backup -m full:
Backs up all database objects. You can make a full backup with or without RMAN. If you do
not use RMAN, then RMAN is called separately to catalog the backup. This means that you
can use this backup as a reference backup for an incremental backup with RMAN.
Syntax: backup_mode = full
In the context of the Recovery Manager this backup is a level 0 backup.