Note that "life on the moon" isn't intended to mean "what daily life on a terraformed moon would look like," but rather "how a terraformed Luna might alter the evolutionary path of the life we bring to it." 

By the time we've completely and successfully terraformed Luna, life will look completely different, both due to human genetic modification and natural selection itself. Even if we made the Moon as Earth-like as possible, some or most of Earth's plants and animals on the moon would change overtime. Plants and animals and humans would all adapt to these minor differences over time. Given a long enough time completely separate from Earth, Lunarians could potentially look rather different from their earth-cousins. Some of these possible evolutionary paths would be an altered diurnal cycle, taller physique(due to the lower gravity), and a larger reliance on plant-matter in their diet(as plant-life is simply easier to maintain in the beginning phases of terraforming).  

Likewise, larger animals could grow taller and thinner, and smaller animals may develop stronger hind-legs to take advantage of the lower gravity's effect on jumping and leap away from predators more easily. 

Such theories are explored in more detail in the Future races and Predictions of future human civilization pages.