Difference between transaction log and redo log in MySQL
REDO log is Oracle terminology, transaction log is InnoDB terminology. Now that all are Oracle engineers, people use both to refer to the same thing in MySQL.

The transaction log is, by default- it can be changed- the two files located in $DATADIR called ib_logfile0 and ib_logfile1. It serves the same functions as the REDO log in other databases- storing writes in a safe way and recovering in the case of a crash, although there are some details in implementation that differ in functionality from other RDMS. It is the main component for InnoDB to be a transactional engine.

Do not confuse the transaction log with the binary logs in MySQL. The binlog, by default, is on the $DATADIR and is *hostname*-bin.index and several *hostname*-bin.00001, etc. It is particular confusing for people coming from other databases, because it is used for other things that other databases use the REDO log for: replication and point in time recovery. The main difference is that the transaction log is InnoDB-only, the binary log is (mostly) transaction-independent, as it is for all storage engines, transactional or not. MyISAM will write (if enabled) to the binary log. InnoDB will write to the transaction log and the binary log.

More info on the manual: REDO log, binary log.