The first approach, demonstrated in the sideways pose, is a transition between two poses. The action is continuous from the beginning position to the final position. Speeded up tremendously, this is the approach taken by movies, TV, and video. They never show movement itself, but show rapid transitions from one pose to the next. The successive poses are called frames. If shown fast enough, faster than about 18 frames a second, the action deems continuous.
This approach works well for movies and TV. Modern movies and videos work even faster, they replace the static image 60 times a second. There is some evidence that muscles work at approximately that speed, i.e. that the tension information controlling the joint angles is updated 60 times a second or even faster. But working at this speed has serious disadvantages. A skilled action lasting twenty minutes would need at least 20 * 60 * 60 = 72,000 poses.
Another problem with this approach is that it cannot be adapted to variations in the action. A walk with arms swinging would need a separate set of poses from a walk without swinging the arms.
The second demo (for the front view) shows how a single motion, that of lifting the arm, can have different rates of progress. If we can make simple contiguous motions slightly more complex, with variable rates of movement, we might be able to capture motion for a longer stretch of time such as a complete stride. That would allow us to put the poses further apart, and thus require fewer of them. A complete stride, even for running, takes at least half a second.
The advantage of this approach is it only requires one or two poses per second. The downside is that the action is synchronized less frequently.