There is a difference between ונתן and וישם (put/place); נתינה requires some minimum amount to be placed.

Furthermore, there is a difference between them in that the verb נתינה focuses on the placement with it and is borrowed from the language נתינה (giving) that is restricted to the opposite of the language לקיחה (taking) to mean anything which is given in a certain place that one rests there. But the verb שימה focuses on the quality of the placement, if there was a certain order and arrangement or a connection with the place, or with respect to the object that is placed - that one was careful in its placement.