I really don't like the "Fluid Style" term anymore or soft. That's an old article.
The way I teach the lifts it is a matter of alignment. I'll give you an example, when you do a snatch, and the bell is back on the swing, the weight is on the heels, but as the weight swings back forward, you shift the weight towards the front of your feet. At this point, it is optimal for you to extend the knees (Like the first bump in the jerk). This does 2 things, it reduces the likelihood that you will pull with the arm (Grip saver) and it also ensures that you will take full advantage of the pendulum effect of the swing.
Fact is that snatches and Jerks are athletic movements (maybe not as complex or as difficult as the barbell versions).
Soft indicates that you should be relaxed. That isn't how it is. I've seen folks be relaxed overhead and rip up their shoulders with snatches. I tell people to actually be aggressive with their fixation of the bell overhead when learning. The only time you can relax is when the bell has actually stopped and it is supported by the skeletal system.
Hardstyle swings were taught in terms of keeping the weight on the heels and thrusting with the glutes. It is ok as an exercise, but had poor carryover to the snatch because the trajectory of that type of swing was out and not up.