I mostly hear about Kiwi politics through a self-described leftist friend who votes ACT so if my perspectives are a bit strange blame them.
"New Zealand is such a progressive country" is a big meme, there are many people even on the Australian Left who fall for it, especially while Ardern was prime minister. Certainly that government tries to look progressive, but its economic system and institutions (with one big exception) aren't much different than Australia's. It's a poorer country and has a lower population than the state of Victoria (5.1 million vs 6.6 million). It's also much less urbanised (Melbourne contains ~75% of Victoria's population, Auckland only ~33% of New Zealand's; adding the next six largest cities bring you up to ~50%) and highly reliant on agricultural exports. And this is an era where left- vs right-wing tribal politics are increasingly defined by the urban vs rural divide, Aotearoa no exception.
What sets New Zealand apart from Australia and other Anglo nations more than anything else is its relationship with its indigenous people (17% of the population). The Treaty of Waitangi (1840) governs the relationship between the British and later New Zealand Crown with the Maori iwis, and it's been interpreted and reinterpreted many times over the years. For many years the consensus, including among Maori leaders, was towards Maori assimilation into the mainstream. In recent years the mood on the political left has swung sharply the other way, every attempt is made to preserve Maori as a distinct society apart from the rest of the country, give Maori preferential treatment (to the extent that people are being prioritised for healthcare solely on the basis of race), and giving iwis more and more say in government outside of the parliamentary framework. The political right has pushed back, demanding an end to "co-governance" and special privileges (the two parties most opposed are ACT and New Zealand First, and both have Maori leaders, who incidentally hate each other)
Labour is your typical centre-left party, says nice things about equality, being for the working class, etc.
National is your typical centre-right party, talks a lot about law and order, stability, looking after farmers and businesses
Greens is the left-wing party, talks a lot about climate change, standing up for the oppressed, Free Palestine, etc. Has only ever been in coalition with Labour.
ACT is the libertarian party, all about cutting taxes, cutting regulations, freedom of speech. Has been in coalition with National in the past.
New Zealand First is the populist party, economically interventionist, socially conservative, anti-immigration, organised around leader Winston Peters who is Trump if he was Maori and actually working class and competent. Has been in coalition with both National and Labour governments (Peters was, no kidding, Minister for Foreign Affairs under two Labour PMs)
Te Pati Maori (Maori Party) is Greens but exclusively Maori, supports the reinterpretation of the treaty system as described above especially in cultural/identity matters, especially under the current co-leaders. Has also been in coalition with both National and Labour governments, although it's undergone a big left-ward tilt as of late.