You pretty much got it in one.
The only difference is that we have no "state law".
There is a common body of law, this law is "Created" up by the central government [i.e. Parliament/politicians].
These laws cover most of the stuff you can get taken to court for like anywhere else in the world:
like killing people, not paying taxes, stealing other folks property, not having a drivers license [and driving on the road], getting married more than once without a divorce in the meantime etc etc - all the laws we live buy.
A few terms are used in that report which may need explaining:
"parole" = Early Release from prison [generally for being a good prisoner, but sometimes because the prisons are full and they don't want to keep you in prison for much longer anyway, or maybe as the holidays are coming up and they want to let you out early to save the hassle of kicking you out on say Christmas day, when everything is shut etc]. If you're on parole and you break the law again (seriously enough), you can be put back in prison - and/or have that time added to your next prison sentence - if there is one.
"non-parole period" = the minimum time in prison you have to serve no matter how good a prisoner you are. If you don't have a minimum non-parole period then you can serve as little as 1/3rd of your prison sentence - if you're really really, nice.
And since we don't have a death penalty, you can't get only 1/3rd killed for being a model prisoner!
In the US you'd say "10 to 20", meaning, 10 years minimum, 20 years max.
Here you'd say 20 years, with 10 "non parole". meaning, you may get out in 10 years, if you're good, but not before.
If you don't have a "non parole" period in your sentence, then you could be out again in 7 and a bit years.
"Diocesan schoolgirl" means the victim attended the local single sex school for "rich parents girls" (boringly its actually called, "The Diocesan School for Girls" - think exclusive Catholic school/college for girls between the ages of about 13, up to the age of about 18 and you're not far wrong.
"Invercargill" is the most southern city in New Zealand - This victim was off to hitchhike over 1,000 miles to the south, by herself, and was murdered less than 20 miles from where she started out from.
BTW: the photo attached to the story makes the One Armed Man look like a three armed man. You can see the arms/hands of the person directly behind him in the photo, but not the person behind him.
Its a odd photo to use, when the caption/story is about a One Armed man!