The rationale in this is that, since changes to data are generally few compared to the entire amount of data in the data repository, the amount of time required to complete the backup will be smaller than if a full backup was performed every time that the organization or data owner wishes to back up changes since the last full backup.
The advantage to this is the quicker recovery time, requiring only a full backup and the last differential backup to restore the entire data repository.
The two terms are widely used in the industry, and their use is universally standard.
All the major data backup vendors have standardized on these definitions.
For example, Oracle Corporation uses a backward description of differential backups in their DB product as of May 14, 2015: "Differential incremental backups - In a differential level 1 backup, RMAN backs up all blocks that have changed since the most recent cumulative or differential incremental backup, whether at level 1 or level 0.