How can the Green party not be part of the coalition if they have Ministers in the government, even thought they are 'outside' cabinet? I'm not arguing the point, I just don't understand how it works.
Cabinet is who make the decisions on the direction the government goes, what legislation is instigated etc. Just like not all labour MP's are in cabinet, it essentially denotes your unwritten 'authority' within the government of the day.
The executive are of the government is made up of Ministers and their departments and should be viewed as a separate body to the legislative arm of government, which includes all MP's, government & opposition.
the executive's role is to decide on policy and if necessary bring forward legislation to enable those policies, the legislative's roles is to scrutinise the actions of the executive.
In answer to your question, being in cabinet is a coveted position because you can influence the direction of the government, but to be a minister is also a privilege because you are responsible for your department and essentially have control of policy within your area of jurisdiction, but to be in cabinet does not require you to be part of the coalition. So for the green's their ministerial posts are just a reward for promising to give heir confidence vote to the labour-nzf coalition