Is marginal cost different from extra cost?
In this graph they use marginal cost to describe a sort of linear approximation of the change in the cost function $C(x)$ at some point $x_0$, that is
$$
MC_{x_0}(x) = (x-x_0) \cdot \frac{\partial C(x_0)}{\partial x}.
$$
This is indeed not the usual way the term marginal cost is used.