Complete backup - In complete backup the entire database is backed up at the same time. This backup includes all the database files, control files and journal files.
Partial backup - Partial backup is not the complete backup of database. Partial backup are very useful in large databases because they allow a strategy whereby various parts of the database are backed up in a round robin fashion on day by day basis, so that the whole database is backed up effectively once a week.
Cold backup - Cold backup is taken while the database is completely shut down. In multiinstance environment all the instances should be shut down.
Hot backup - The hot backup is take when the database engine is up and running. Hot backup requirements that need to be considered vary from RDBMS to RDBMS. Hot backups are extremely useful.
Online backup - It is same as the hot backup.