I have lived in various parts of the United States, from the deep south to the San Francisco Bay Area. Everybody always called it the grocery store. The only times I’ve heard it called a supermarket have been in movies or TV shows. What do you call it?

ETA: I understand context matters. For example, if I am just running out the door to pick up one or two things I will probably say I’m going to Kroger, Publix, wherever. OTOH we recently we were on vacation. We discussed needing to find a "grocery store" not a "supermarket"! It's very location dependent. I didn't know what chains or locally owned stores might close by. So we used grocery store.