Is “simple story” the same as “crude,” and is “formulation” the same as “story”?

No. They overlap, but they are not identical.

Simple

Simple means containing relatively few elements or steps.

A simple explanation can actually be perfectly accurate.

For example:

“The Thirteenth Amendment abolished slavery.”

That is simple, but not crude.

Crude

Crude means insufficiently refined, nuanced, or precise.

For example:

“The Thirteenth Amendment gave Black Americans equality.”

That is crude because it collapses legal abolition, citizenship, political rights, economic equality, social equality, etc. into one proposition.

Story

Here story means a narrative account of how events happened.

For example:

“Slavery was abolished, freed people became workers, and capitalism made them middle class.”

That is a historical story.

Formulation

Formulation means the particular way in which an argument or proposition is expressed.

So:

• story = the narrative/argument you are presenting;
• formulation = the wording or conceptual expression you use to present it;
• simple = relatively few elements;
• crude = insufficiently nuanced or precise.

A story can be simple without being crude. A formulation can be concise without being simplistic.