You would have to ask whoever wrote the requirement what they intended by using the word "generic". My guess is that they were using "generic" to mean "not an application DBA and not a development DBA". But that's just a guess. As with all job descriptions, there is no single definition that everyone will agree on.
How should be difference between them , if the generic oracle DBA not exists ... But i am guessing here it will not be specific Job for database administration , it will include lot of other tasks that not related to DBA . (But like i told nothing called Generic DBA Google it to make sure ) , so maybe will do some administration , networking , development
I googled genaric oracle dba, and it seems there are places in India that are using that term to refer to basic dba skills. There are also places that make postings that have a bunch of random search terms in there, with no time limit on the post, spinning forever in the cybersphere. So you wind up seeing results like "Oracle DBA - Bangalore - Internet Jobs - GENERIC VIAG RA ORACLE" because it has the terms generic and via gra in the post. There is, indeed, no upper limit to recruiter stupidity.