These 2 are different, doesn't have any implication on each other. One is API and other is oracle proprietory software for communication across database and its client. This is the general standard of Industry applications, I guess nothing to do with issues you have with dead connections

ODBC:

Open DataBase Connectivity (ODBC) is an Application Programming Interface (API) that allows a programmer to abstract a program from a database. When writing code to interact with a database, you usually have to add code that talks to a particular database using a proprietary language. If you want your program to talk to an Access, Fox and Oracle databases you have to code your program with three different database languages. This can be quite the daunting task causing much grief. Now, enter ODBC...

When programming to interact with ODBC you only need to talk the ODBC language (a combination of ODBC API function calls and the SQL language). The ODBC Manager will figure out how to contend with the type of database you are targeting. Regardless of the database type you are using, all of your calls will be to the ODBC API. All that you need to do is have installed an ODBC driver that is specific to the type of database you will be using.

Net8/SQL*Net:

Oracle's remote data access software that enables both client-server and server-server communications across any network. Net8 supports distributed processing and distributed database capability. Net8 runs over and interconnects many communications protocols. Net8 is backward compatible with SQL*Net version 2.