The flail is a medieval weapon made of one (or more) weights attached to a handle with a hinge or chain. There is some disagreement over the names for this weapon; the terms "morning star", and even "mace" are variously applied, though these are used to describe other weapons, which are very different in usage from a weapon with a hinge or chain, commonly used in Europe from the 13th century to the 15th century. In construction, the morning star and flail have similar, if not identical, spiked heads. Thus, morning star is an acceptable name for this weapon, especially as the name "flail" is also used to describe a style of whip used for flagellation.
The term "morning star" actually refers to the head of a weapon (the small round spiked ball) and can be used for either a morning star mace (on a shaft) or flail (if on a chain). Flails also sometimes had blunt round heads or flanges like a mace. Some written records point to small rings attached to chains on a flail used to inflict greater damage, but no historical examples are known to exist.
I can just picture the geeky kids (I knew several of exactly the type!) who'd been referring to the spike ball tipped flail as a morning star all their lives now spitting up their Fritos in indignation.