Does anyone know what is the difference between IDMS and DB2?

Answer 1

IDMS is a Network Database Management System (NDBMS).
DB2 is a Relational Database Management System (RDBMS).
RDBMS is a DBMS in which data is stored in the form of tables and the relationship among the data is also stored in the form of tables.
NDBMS is a set of records which is having owner and member relationship within the set.

Answer 2

IDMS is one example of DBMS, called Network DB. DB2 is the main Relational data base management system.
They are very different in term of:
design of data base, access. DB2 is product of IBM, but IDMS was product of old old Cullenet company. Look for Network DBMS and find articles of IDMS. 

Just for the information, IMS (from IBM corp) was one of the main DBMS and is still used in major corp in US.