Does dbms create separate files for index entries and data?

In general in different DBMS systems different storage engines store data differently. Oracle would store table and index data in tablespaces. Tablespace can use one of more data files. Table Data and Index Data can be stored in the same or different table spaces - per DBA's discretion. Oracle also has way to mix index and data together for better performance - check out Index Organized Tables (IOT) MySQL MyISAM  storage engine has ability to store table and index data in separate files and InnoDB also uses tablespaces. DB2 Database also can store table and index data either in individual files or in tablespaces.

MySQL's MyISAM does. It's implementation dependent.

As many have noted, it's entirely implementation dependent. However, the differences mean less than you might think. Whether you use separate files, or have one big file and use your own mechanism for keeping track of which bits of the file contain what and management of free space, it all just comes down to blocks scattered on the disk. If you use separate files, you're making use of the filesystem's inbuilt ability to split the disk into logical files and manage free space. If you use one big file, then you're doing it all yourself, and just using the filesystem as a pool of storage you can request new blocks from (by growing your file), and maybe release them back if you feel genorous. If you go the whole hog and access raw partitions, that's not much different to just using a single large file, except that your free space can't be used by other applications and you might get better control over write caching (which can speed up commit times, but that's another matter). So, clearly, it only makes a difference if you do a better or worse job of it than your filesystem! Using the filesystem may not save you much code, as you probably need free space management within your index/table files anyway to handle deletion of records. But it can still simplify your code when it comes time to drop entire tables or indexes, as you can just ask the filesystem to unlink the entire file, rather than needing to scan through the thing you're deleting and add all its pages back to your own free list. Whether your own bulk-deletion system is more or less efficient than the filesystem's is another question entirely!