java.sql is the package you can use for all basic kinds of database access. If you are not developing a full scale enterprise application, java.sql package is all that you need.
javax.sql is extension to the basic java.sql package. It includes classes that allow connection pooling and rowsets, among others.
If you are just getting started with JDBC, you just need to get familiar with java.sql and leave the wonders of javax.sql until later.