I like to buy food at my grocery store. It makes shopping easy.
Well they  primarily sell food.
I like to find fresh fruits and vegetables there as well. Also, the deli has great meats.
Well  Grocery stores often offer non-perishable food that is packaged in bottles, boxes, and cans
Yeah those are great for when we need food that will last on a shelf. No refrigeration required.
I have heard Small grocery stores that mainly sell fruits and vegetables are known as greengrocers