Definition of "differential"

Question

I am confused about the definition of "differential".

Sometimes I see it is a pushforward mapping $df:TM\rightarrow TN$, which gives another tangent vector when acting on a tangent vector.

https://en.wikipedia.org/wiki/Pushforward_(differential)

Sometimes it acts as a cobasis in contangent space, which contracts with tangent vectors and gives a real number, $df:TM\rightarrow \mathcal{R}$

https://en.wikipedia.org/wiki/Cotangent_space

How are the two definition compatible with each other?

Thank you very much.