"People" or "peoples" when referring to an indigenous population?

Let's say we are talking about the indigenous pukapuka who live in Pluto.

What is correct: "the pukapuka people" or "the pukapuka peoples"?

I've read somewhere the usage of "peoples" in this context, and it has surprised me.

Solution 1:

"Peoples" means a group of populations. So for example "the native American peoples" means the tribes that were living in America before Columbus. "the pukapuka peoples" would mean "the group of tribes/groups collectively known as pukapuka", whereas "the pukapuka people" would mean "the group of people known as (the) pukapuka (tribe/group/etc.)"