Recently I was told (by an algebraic geometer) that when algebraic geometers look at the Calculus of Functors, they think of stacks.

When I look at the Calculus of Functors, I see a categorification of polynomial approximation. While I am at best a beginner at algebraic geometry, I would like to understand why he is saying this.

My motivation is twofold. First, I want to know why he is saying this, and second, because I am beginning to learn about stacks, and I want to come at it with some intuition. I have pursued the obvious routes of reading about them in general (such as Tolland's Blog Post).

Specifically, my question is

How does one see Calculus of Functors as stacks?

A secondary question,

Is there some highly degenerate way to look at stacks to see polynomial approximation?

Thanks!