Answering only the MySQL Part of the Question
A binary log records completed SQL statements. You can have many binary logs. Under default settings, binary logs rotate at the 1G mark (see expire_logs_days and max_binlog_size).
You can see binary logs by running one of the following:
SHOW BINARY LOGS;
SHOW MASTER LOGS;
Ther current master log is always the last one in the list. To see just the last binary log, which is the current one, run this:
SHOW MASTER STATUS;
When it comes to InnoDB storage engine and transactions
- There is a metadata file (ibdata1, which holds, by default, data pages, index pages, table metadata and MVCC information), also known as the InnoDB tablespace file.
- You can have more than one ibdata file (see innodb_data_file_path)
- There are redo logs (ib_logfile0 and ib_logfile1)
- You can have more than two redo logs (see innodb_log_files_in_group)
- You can spread data and indexes across multiple ibdata files if innodb_file_per_table is disabled
- You can separate data and index pages from ibdata into separate tablespace files (see innodb_file_per_table and StackOverflow Post on how to set this up)