JDBC is a long-established standard used in Java to access SQL databases. DB Vendors implement a JDBC driver so that all DBS can be accessed in a uniform manner. Practically EVERYTHING done with databases in Java USES JDBC.
JDBI is a convenience library built on top of JDBC. If your database has a JDBC driver, you can use Jdbi with it. JDBI is a performant, production ready, EASY to use library that takes the pain out of JDBC.