current PhD applicant applying to another university
Yes.  If you are a student, you should say so in your application.  Otherwise, your CV will have an unexplained gap for the time you've been at your current department.  Unexplained gaps raise red flags with admissions committees.

In your statement, you also need to explain why you are applying to the new department instead of completing your PhD at your current department.  Moreover, you must do so without disparaging your current department, even if you have legitimate cause to do so; nobody likes a whiner.  Good reasons to move include a change in your own research interests, your advisor moving or retiring, following a spouse.

Above all, do everything above board.  If possible, you should also request at a recommendation letter from your current advisor; if not your advisor, some other faculty member in your department.  If you apply secretly, you risk burning all bridges with faculty in your current department.

Credit transfer is a completely orthogonal issue.