I live in Vancouver. In North America, particularly in the United States and Canada, the term "grocery store" is commonly used as a synonym for "supermarket." Most people would refer to a large chain store like Safeway as a "grocery store," even though they fit the technical definition of a supermarket. Supermarkets are characterized by their self-service model, a much larger retail space, and an extensive range of non-food items available for purchase In other parts of the world, such as the United Kingdom, the distinction can be more evident, with "supermarket" being the more common term for large-scale grocery retailers, while "grocer's" might refer to a smaller, more traditional food shop.

Native English speaker from the Philippines here. For me, “supermarket” and “grocery store” mean the same thing. I think one term may be used more commonly than the other depending on where you live. Personally, I’ve seen both terms used interchangeably in the Philippines.

Historically, a "grocery store" should sell mostly food whereas a "supermarket" should sell food plus other household items. However, in the modern sense they are largely interchangeable and often dictated by region, dialect or simply personal preference.

I'd say they're the same thing but different regions use different terminology. In the UK, we say 'supermarket'. 'Grocery store' is understood but not really used. (The word 'store' isn't used much in the UK. We use 'shop'.)

Maybe grocery store is more common especially in Canada. Maybe my grandparents would call it a supermarket, not to say that supermarket sounds old, but I don't think I would ever day it.