In the US, we call the first item you demonstrated a hank. (Technically, a hank is a variety of skein.) In the US, a skein is yarn wound into an oblong, often by machine. There seem to be manufacturing standards as to weight and length depending on the yarn thickness. (When I was a kid, skeins were not sold as center pull, and were often wound into balls to be less prone to twisting and tangling.) A ball is often hand wound, and generally spherical. The lengths and weights are more variable, but often considerably less than a skein. A cake can vary from in size from ball to skein; it's wound to sit flat and be easier to control.
