I've really only seen "Pumpkin" used more commonly in Australia, where I was surprised to see someone refer to what I knew as a butternut squash as a pumpkin.
As per https://www.epicurious.com/ingredients/what-is-in-canned-pum... the company responsible for 85% of the world's canned "pumpkin" doesn't actually use the type of squash you're likely envisioning (and links the FDA docs allowing a variety of squash to be labeled as such: https://www.fda.gov/regulatory-information/search-fda-guidan...), and the type of squash you're likely envisioning having a fairly mediocre flavour relative to the alternatives.
In a sense I think you're both completely right and completely wrong in different ways.
Pumpkins were always the orange, large and round ones - and back in the 80s we still carved turnips or swedes in the North of England, as pumpkins were too expensive.
TL;DR all pumpkins are squash, but not all squash are pumpkins.
Ok, according to Wikipedia:
> A pumpkin is a vernacular term for mature winter squash of species and varieties in the genus Cucurbita that has culinary and cultural significance but no agreed upon botanical or scientific meaning.
So "pumpkin" is the more widespread term (at least that's my feeling?), and it can be applied to all "squashes", but it's not scientifically correct?