Databases – Doubts about the definition of partial functional dependency.

I have some doubts about the definition of partial functional dependency.
According to the book Fundamentals of Database Systems by Elmasri and Navathe.
The definition of partial functional dependency is

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

Now, on many websites on the Internet and even teachers in my class are saying the following definition of partial functional dependency.

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

Now, the problem occurs when a question is asked so

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

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

So, which one is correct?