First Movie: Weight trainer style dumbbell raise.
Note the arching of the back and the rotation of the trunk as the dumbbell is lifted. (picture sourced from http://www.exrx.net/WeightExercises/DeltoidAnterior/DBFrontRaise.html)


Second movie: Pilates style dumbbell raise.
A smaller weight is used and there is strict attention to awareness and stability at the core.
Notes:
It may appear that I am singling out www.exrx.net for criticism. Not so! What you see in the upper movie I see every time I walk past the weight training room on my way to my pilates workout. And this is happening in a highly reputable fitness center. This author wishes to thank www.exrx.net for their excellent library of weight training information.