Greenstone / Pounamu / Jade are often the same thing from different angles.
As a Pakeha carver I would avoid defining Pounamu from a Māori point of view. As a New Zealander it generally means NZ Jade but includes some serpentines (a common green stone). Tangiwai (Bowenite) is the most common type of serpentine that described as Pounamu. It is a really translucent and has an amazing beauty of its own. It is rare to find good examples and is highly treasured. You can see photos of different types of Pounamu Here.
I’ve heard greenstone is the term Captain Cook used to describe Maori Jade carvings. It’s a term that is only used in New Zealand/Australia and can be confusing in nature as we have a lot of “green” stones. I think slowly New Zealanders are starting to use Pounamu instead of greenstone.
Jade is the common word for nephrite. It is used worldwide and is specific. Internationally the term Jade is used for two different stones – Nephrite and Jadeite. In New Zealand all our Jade is Nephrite but overseas the term Jade could be used for either depending on where you are. You can read more about Jades from other countries Here.
Jadeite is a semi precious stone. It doesn’t occur naturally in New Zealand. It is harder than Nephrite and comes in a range of colours a little different. Along with white and green, jadeite comes in reds, lavenders and yellows. You can read more about Jadeite Here.
So as you can see the terms jade, pounamu and greenstone can often be used for the same stone,
– I would use Pounamu to describe NZ Jade (Nephrite) + some high quality Serpentine’s.
– Greenstone should mean the same thing as Pounamu.
– Jade could refer to Pounamu or other jades from overseas (Nephrite and Jadeite).