Is there anyone on the Coast who does this?
Sometimes the honest answer is that the nearest is in Christchurch or Nelson, and the quote should say so with travel in it. NovaPay asks locally first and tells you when it has had to look further rather than quietly widening the search.
Carpenter or builder?
A carpenter is the right call for defined joinery and finishing work. Once the job is structural, involves weathertightness or needs consent, it is building work and may need a Licensed Building Practitioner. Describe the job and the replies will tell you which it is.
Can they make something to fit?
That is the advantage over flat pack. An alcove that is not square, a sloping ceiling, an awkward corner: those are exactly where built-in beats bought-in.
Who supplies the timber?
Usually the carpenter, and it is worth having it stated. Some will happily fit materials you have bought, though most prefer to supply so they can stand behind the result.
Is a small job worth calling someone for?
Most carpenters have a minimum of a few hours, so a single door is expensive on its own. Save the small jobs up and ask for them together, the same way you would with a handyman.