Full vs Fast-path vs HALDB vs DEDB

IMS DB and DB2 both are databases. The DB2 is RDBMS whereas IMS DB is a Hierarchical database.

4 Types of IMS DB Databases

Full function databases can have primary and secondary indexes, accessed using DL/I calls from your application program, like SQL calls to DB2 or Oracle.
Full function databases can have a variety of access methods, although Hierarchical Direct (HDAM) and Hierarchical Indexed Direct (HIDAM) dominate. The other formats are Simple Hierarchical Indexed Sequential (SHISAM), Hierarchical Sequential (HSAM), and Hierarchical Indexed Sequential (HISAM).
Full function databases store data using VSAM, a native z/OS access method.

Fast Path databases are optimized for extremely high transaction rates. Data Entry Databases (DEDBs) and Main Storage Databases (MSDBs) are the two types of fast path databases. Neither provide any indexing. Virtual Storage Option (VSO) DEDBs can replace MSDBs in modern IMS releases, so MSDBs are gradually disappearing.

IMS V7 introduced HALDBs, an extension of IMS full function databases to provide better availability, better handling of extremely large data volumes
With IMS V9, online reorganization to support continuous availability. (Third party tools exclusively provided online reorganization prior to IMS V9.) .
A HALDB can store in excess of 40 terabytes of data.

Fast path DEDBs can only be built atop VSAM.
DL/I databases can be built atop either VSAM or OSAM, with some restrictions depending on database organization.
This “limitation” simply means that IMS customers will use multiple datasets for large amounts of data. VSAM and OSAM are usually referred to as the access methods, and the IMS “logical” view of the database is referred to as the database “organization” (HDAM, HIDAM, HISAM, etc.) Internally the data are linked using 4-byte pointers or addresses.
In the database datasets (DBDSs) the pointers are referred to as RBAs (relative byte addresses).