Military personnel are shopping
Military personnel are buying groceries.
shopping doesn't always mean  buying groceries.
The personnel might not be buying groceries, but other items, like clothes.
Shopping has a slightly different meaning from buying; to be buying means to be in the act of paying while to be shopping can mean to be looking at things with the intention to be buying at some time either now or in the future; there are many products that one can shop for and groceries are only one of them.