Mysql: binary log vs transaction log
The binlog is a history of the writes to the database.  It is vital for replication.  It can also be used in certain "incremental" backup techniques.

The transaction log (usually in files iblog1 and iblog2) is vital to InnoDB for multiple reasons:  ROLLBACK, crash recovery, and possibly more.

Manual page about binlog 
non-InnoDB logs

Redo log

There are lots of web pages discussing these files from various viewpoints.

There are many ways to do "backup".