Although it's a bit rough to call them common - take a squiz at this map from Te Ara showing pukeko distribution across New Zealand - its hard to find a place where they're not kicking up a storm in a wet spot!
If you're lucky enough to see a takahē (the best place to see them in captivity is Mt Bruce in the Wairarapa) it's about three times the size, has a tealy-green back (instead of black), and shorter, heavier legs. Sadly, there was once another close cousin in the pūkeko family - the moho (or North Island takahē) which is now extinct and only known from skeletal remains.
The pūkeko and takahē are believed to have descended from two quite separate invasions of the same ancestral bird: the Purple Swamphen from across the ditch (Australia). Pūkeko ancestors appeared to have arrived here about 1000 years ago, whereas those of the takahē are thought to have flown in more than 10 million years ago!
Although the takahē has kept its wings, over many generations evolving in the peaceful and predator-free ancient Aotearoa, it slowly lost its ability to fly.