Before knowing the difference between Oracle DBA and Oracle EBS DBA, you should know that basically there are two types of DBA:

Core Database Administration
Application Database Administration (like SOA, EBS, PeopleSoft, etc ..)
Oracle DBA might be Core DBA or Application DBA. We can differentiate these DBAs as per their responsibilities.

Role of Oracle Core DBA:

Installation/Upgrade of Oracle Database.
Database user creation and deletion
Roles and Privilege management
Application of Oracle Patches to database
Database Backup and Recovery , etc..
Role of Application(EBS or APPS) DBA:

Install and Upgrade EBS application
Cloning of Application
Apply patch to the Application
Fixing of Oracle Form Browser Issue, etc ...
As I have not worked much as Oracle Apps DBA, so I can not tell you in detail. An Oracle APPS DBA generally perform both roles. As per the project, there will be different DBAs for each role.

But if you are going to be an Oracle APPS DBA, you should have good knowledge of Oracle Core Database.