The first sense of reasoning is the wider one.

Note that in that sense nothing is said what these ideas must be, nor by what process one arrives at these, whether deductive, inductive, abductive or otherwise. It is not even said whether reasoning is conscious or not.

And indeed, it makes sound sense to insist that writing a piece of fiction, deducing a theorem, thinking of what to eat for dinner, and falling in love all involve some sort of reasoning.

The second sense of reasoning is a bit more restricted in that it explicitly refers to inferences, conclusions and assumptions.

In the second sense there still is no notion that the reasoning is conscious or involves languages, or explicit premisses, since the assumptions one uses may well be unconscious, imprecize or unverbalized.