The Others come from beyond The Wall and are currently most powerful in that realm. They can't, as yet, cross The Wall. They can resurrect people/animals as Wights directly. People who die North of The Wall generally seem to rise as Wights due to the presence of The Others in the region which is why the Wildlings burn their dead.
The Ranger that attacked Mormont died beyond The Wall and was one of Benjens men. Now we know that they were attacked by The Others. The men who died in battle at Winterfell are not near The Others or their magic so haven't risen as Wights.