Essentially, yes. The key is intent. A lot of people simply do an exercise in any way they can, or whichever way they happen to do it (I would say “naturally”, but many people in modern societies have poor movement patterns due to leading unnatural physical lifestyles [sitting down with poor posture for hours, rounding their backs when they bend down to pick something up, etc]). But in doing so they could be (and often are) missing out on some of the benefits of the exercise.
The reason I gave the idea of little men at the bottom of your sternum pulling your legs up with a rope that’s connected to your pelvis is because it’s an easy way to pretty accurately visualize the control of the contraction of the rectus abdominis.