Collection Database
The collection database dictates how data about your collection is stored. Greenstone comes with two database options: GDBM and JDBM. They are essentially the same; JDBM is simply a Java implementation of GDBM. They are flat file database engines. You can select which of these to use in the Browsing Classifiers section of the Design panel.
It is also possible to use a relational database system, like Microsoft SQL (MS-SQL) to create your collection's database. Some notes on configuring Greenstone to achieve this are here.
GDBM
GDBM (or GNU Database Manager) is a simple flat-file database engine which Greenstone uses as the default database for new collections.
JDBM
JDBM (or Java Database Manager) is essentially a Java implementation of GDBM. Consider using this database engine combined with the Lucene indexer if you are wanting to create a pure Java run-time.