These ‘general’ strength workouts are intended as conditioning to prepare on for more demanding work later. There are more ways to do this kind of thing than you can shake the proverbial stick at. Hence the variations in the descriptions you mention. There is no ONE way to accomplish this task. A seasoned athlete with significant strength training background might no even use this phase unless he/she has had a long break.
So, don’t get bogged down trying to parse sets and reps too finely. The Strength world can split hairs over sets and reps ad nauseum but I have seen great real world results come from a wide variety of prescriptions. For this kind of conditioning work it’s just not that important. As we mention in the book and elsewhere: These exercises and routines are not a magical combo. They are just some we have use to good effect. Think big picture.