databases – Doubt about definition of partial functional dependence

I have some doubts about the definition of partial functional dependence.
According to the book Basic Principles of Elmasri and Navathe Database Systems
the definition of partial functional dependency is

A functional dependence X -> Y is a partial dependency if an attribute A belonging to X can be deleted from X and the dependency is still valid; that is, for some, A belongs to X (X – {A}) -> Y.

Now, on many websites and even my class teachers we explain the following definition of partial functional dependence

Partial dependency is a type of functional dependency that occurs when one of the non-key attributes is dependent on the subset / part key of candidates.

Now, the problem arises when a question is asked like this

Let R (A, B, C, D, E) be a relational schema where {A, B} is a candidate key, the functional dependence B-> C being a partial dependency or not.

According to the definition of the book B-> C is not a partial dependence, but according to my class, teachers B-> C is a partial functional dependence.

So, which one is the right one?