Actually no, neither of your flywheels is an Arctic flywheel. Stihl switched to the "lightweight" flywheel as a part of the transition to the MS-440. That would be the flywheel on the right in your picture. The older style, i.e. the flywheel on the left, is the regular flywheel that came on all 044s (even 10mm wrist pin saws) up until the transition to the MS-440.
In order for a flywheel to be for an Arctic model, it has to have the inner magnets like the one you found on ebay. There's a generator that fits inside that magnet structure that makes the voltage powering the Arctic accessories. I considered using the Arctic generator to power a light for night time operations on forest fires.
