I have used the big sheets of very cheap thin card board...not corrugated, just one ply...that the feed stores get with their pallets of feed. It is placed between layers of bags at the mill, I guess, and the store just throws them away. So they are happy for me to take it.
It doesn't hold up very long, and I'm not sure how it would do under wood chips. The chips might poke right through it after walked on a few times. I use it under straw or pine needles.
My old standby is newspaper, multiple layers.
we snag boxes and those layers too at times when we go to the big box stores... i always avoid anything shiny and printed on now if i can help it. having to remove shredded bits of plastic from a garden isn't any fun at all...
yes, newsprint is often ok for such uses too, as an extra cusion i put it under cardboard layers if i want the path way liner to last longer.
around here we have much harder surfaces and often bits of gravel so even black plastic thick layers will get rocks poking through them at times. to cushion that i will use cardboard or newspapers.
the idea with craft paper is that sometimes people don't have easy access to clean/free cardboard and it could be used instead.
i just like that after a few seasons the worms take care of it and you only have then a woodchip pathway to maintain. making humus...

once the woodchips have mostly decayed and been topped off a few times (to keep the wood chips thick enough to prevent easy weed sprouting) that pathway humus can be used by scraping back the top layer of undecayed wood chips and then lightly scraping off the humus that has formed. black gold for many gardens.
scraping lightly doesn't disturb the underlying soil much so that prevents moving weed seeds back into the germination layer.
then just put the undecayed wood chips back and top off as needed until next time.
the craft paper is your temporary light block and to smother any weeds there. you may have to do this more than once for stubborn weeds, but that's a minor thing to me vs. the mess that black plastic can make.
in our gardens/decorated areas a lot of the spaces and pathways are underlaid by old carpetting. some of it is holding up just fine and i may never have to replace it. in other parts it's gradually falling apart and getting more holes through it that any weeds will exploit. i have some really indestructable materials i can use any time i want to redo an existing area if we want to keep it clear of weeds and put back the crushed limestone, but i'm trying to reclaim areas for growing things if i can so getting those layers of stuff out of the way can really be a messy issue.