There are a few different nomenclatures: some institutions have a letter grade system (Scientist C, Scientist D, and so on); others have entry level positions called lecturer/fellow/reader/assistant professor, which at more senior levels become less varied, settling at the more familiar Associate Professor, Professor etc.

The good part is that the applicant does not need to know the name of the position they will be considered for. Each institution has rules that indicate what level a person can be considered for. As an example, if an Institution's rules are that 10 years post PhD experience corresponds to an Associate Professor designation, such an applicant cannot be considered for a more junior appointment,and can only very rarely, with exceptional qualifications, be considered for a more senior appointment. The system does not allow negotiations, and likewise, cannot be unfair to an applicant either.

Bottom line: the level of appointment is not something that needs to be (or can be) negotiated, but you don't have to worry about getting a fair deal either- each applicant will be considered for an appropriate as per an institution's rules. So you can just state that you wish to apply for "an independent investigator" position and let the system take care of it.