Because I've heard too many people referring to Walmart and Target as grocery stores rather than hypermarkets.

Would I confuse you Americans if I use that word to describe Costco?
I believe you are referring to hypermarket, which is technically correct, but it is not commonly used in the U.S. Superstore is a very common term, especially for Walmart.
A grocery store is (in a strict sense) only selling groceries (food). Supermarket originated as a term to describe large grocery stores that sold kitchenware, over-the-counter drugs, greeting cards and other items that are bought frequently.

Hypermarket recently originated as a term to describe a very large store that sold many other types of household items - electronics, furnishings, clothing, etc.
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"Big box" is what I most often hear stores like CostCo, Target, and Walmart called.
Vorpar"Big box" is what I most often hear stores like CostCo, Target, and Walmart called.
Yes the stores are very boxy - they look like big boxes, and they sell items in large quantity units (Big Boxes).