Full backup, Differential backup and Transaction log backup

Full backup

A full backup contains all the data in a specific database or set of file groups or files, and also enough log to allow for recovering that data. It is the base of both differential backup and transaction log backup.

Differential backup

A differential backup is not independent and it must be based on the latest full backup of the data. That means there should have a full backup as a base. A differential backup contains only the data that has changed since the differential base. Typically, differential backups are smaller and faster to create than the base of a full backup and also require less disk space to store backup images.
Therefore, using differential backups can save available space and speed up the process of making frequent backups to decrease the risk of data loss. At restore time, the full backup is restored first, followed by the most recent differential backup.
Remember not to rely on only one base, create several base of differential backup at different times to guarantee the backup files' security.
 
Transaction Log Backups (Full and Bulk-Logged Recovery Models Only)
 The transaction log is a serial record of all the transactions that have been performed against the database since the transaction log was last backed up. With transaction log backups, you can recover the database to a specific point in time (for example, prior to entering unwanted data), or to the point of failure.
The transaction log backups are only valuable under the full recovery model or bulk-logged recovery model. Each log backup covers the part of the transaction log that was active when the backup was created, and it includes all log records that were not backed up in a previous log backup. An uninterrupted sequence of log backups contains the complete log chain of the database, which is said to be unbroken. Under the full recovery model, and sometimes under the bulk-logged recovery model, an unbroken log chain lets you to restore the database to any point in time.
Just like differential backup, transaction log backup is also based on full backup. Therefore, before you can create the first log backup, you must create a full backup, such as a database backup. Because it requires less disk space than full backup, you can create them more frequently than database backups.