Dear Demetrio Frattarelli,
usually, these two type of squat jumps (for example, see in YouTube Barbell Squat Jumps and Barbell Jump Squat) are carried out with different overload weight and with different training aim.
The execution technique of these two exercises must be determined by their training aims. Before the execution of these exercises their aims must be explained to the athlete.
Barbell Squat Jumps are executed with the weight that must be selected according to the athlete’s abilities within the limits of 30-60% of maximum. In one set there are 4-6 squat jumps. Each jump must be performed with the aim to jump highly.
So, Barbell Squat Jumps must be normal vertical jumps with previous concentric phase that can assure the best height. After each single jump lending, the athlete must stop and relax (shake) the legs, one after another. In the case of very heavy overload weight, before each single squat jump repetition, the athlete can rack the barbell.
Barbell Jump Squats are executed only with barbell on shoulders (it could be light barbell of 10-15 kg weight or the heavy Olympic barbell of 25 kg weight). Usually it’s used 10 – 20 consecutive jumps with the aim to maintain the constant jumps height, legs flexion and vertical back position. This exercise is usually used as training mean for the improvement of Local Muscular Endurance and Maximal Anaerobic Power.
Barbell Jump Squat could be used as explosive strength mean:
1) by athletes with low level of special strength preparedness, who never used squat jumps with overload or
2) by athletes with high level special strength preparedness, at the beginning of the SST preparation cycle, before to use Barbell Squat Jumps.
So, the kind of overloaded squat jumps to be used depend on the training aim, the level of athlete and the temporal placement of these exercises in the training plan.