They are two different sets of standards (ODBC from microsoft and JDBC from Sun) that were created so that Developers can write code that could use a standard set of API calls from their programs and talk to any database using a suitable driver which could translate the API (which was fixed across all vendors) calls to Database specific protocols (which was vendor dependent)(save JDBC type 1&3 drivers which had other tiers doing that work of translation to DB protocol).
Now the implication of all that is, if you developed a program using JDBC API, and oracle as backend, you could port it to Teradata with almost no effort, as long as you haven't written any oracle specific SQL. The only changes would be in the connection string and you would have to load the right driver for the database.
Though it's not my area of expertise, I wouldn't think these two are related. Websphere is an application server, so you have your Java applications running on it. And those java applications may use JDBC if they need to connect to the database.
JServer, as far as my knowledge goes, is an oracle attempt in providing a "built in" compiler inside the database, which enables the programmers to write code in the database (like procedures, triggers etc) in java. It doesn't have anything to do with JDBC.