JDBC abbrevated as Java Database Connectivity.It can connect to any relational databases, such as Oracle,MySQL,Sybase etc., In-memory relational databases such as derby etc., Most of the relational databases implemented using C/C++ languages , and runs in different address spaces. In order to communicate with any database client must have a JDBC Driver. This driver is proprietery from specific vendor, and also freely downloadable. JDBC Driver converts JDBC API calls to database calls.Drivers are available from specific vendor sites.
JDBC API is part of Java SE framework, it acts as an abstract to connect to any database. It has set of classes and interfaces.Actual implementation of JDBC API done at Driver software(.jar) side. These drivers are different from each vendor. and also version specific.
Where as In-memory databases like derby has built-in JDBC driver,and implemeted it as a pure java JDBC driver