Grocery/groceries = items of food sold in a grocer’s shop such as flour ,sugar, tinned food etc.

Green grocer = shopkeeper selling vegetables and fruit.

Related usages :  to the grocer/to the grocer’s = to the grocer’s shop.

• He has gone to the grocer’s.
• Similar usages :  to the baker/ to the baker’s
• Are you going to the baker/to the baker’s?
• to the butcher/to the butcher’s
• to the doctor/to the doctor’s.

Provisions = (plural) supplies of food and other necessary things such buckets, cups and detergents etc

• Provisions for journey.( Not provision)
• But , a provision merchant/shop. ( Not provisions)
• Note:-  All groceries can be provisions, but all provisions are not groceries.