Okay, so in Griffiths' Introduction to Electrodynamics, Griffiths clearly defines surface current density as follows:
when charge flows over a surface, we describe it by the surface current density, $K$. Consider a 'ribbon' of infinitesimal width dL running parallel to the current flow. If the current in this ribbon is $dI$, surface current density is $K=dI/dL$.
Now, I searched Google and some websites which are clearly telling me that surface current density is current per unit AREA, not length! Is there something wrong with my understanding of this concept or are both the definitions equivalent?
Griffiths similarly defined volume current density as current per unit area perpendicular to the current flow, while in my opinion, it should be current per unit VOLUME...
This is really very confusing to me, please clarify.