Backup :

Full database backups: A full database backup copies all data from the database pages to including all objects, system tables, and other data. The Transactions that occur during the backup are also recorded. Full database backups allow you to perform a complete restoration of the database as it existed at the time the backup operation is performed.

Differential backups: They back up data that has altered since
the last full backup. Differential backups require less time than full database backups.

Incremental backups: An incremental backup backups and saves everything that has changed since the last backup of any type whether (full or differential).

For example, suppose that you do a full backup every Sunday.

On Monday, you do a differential backup of everything that has changed since Sunday.

On Tuesday, you have two choices: you can back up everything that’s changed since Sunday (differential), OR  you can back up only the data that has changed since Monday’s backup (incremental).

Transaction log backups :   transaction log backup records all the changes that have
occurred since the previous transaction log backup and then truncates the transaction
log. A truncation removes transactions from the log that have been committed to the
database or cancelled. Transaction log backups use incremental way as the logs are stored in sequence.

File and filegroup backup : This type of backup is intended to increase flexibility in scheduling to full backups, in particular for very large databases. File and filegroup backups are also useful for large databases that contain data with varying update characteristics meaning, some filegroups allow both read and write operations, whereas some are read-only.