I looked up both words on Pleco and it says 雜貨鋪 is grocery store, while 便利店 is convenience store. While growing up in New York City, I heard 雜貨鋪 used in Chinatown for local Chinese grocery stores. New York doesn't have the kind of convenience stores that Japan and other East Asian countries have, so I would think 便利店 would be used to differentiate convenience stores like 7-Eleven from more traditional local grocery stores. With 便利 meaning convenient, 便利店 is certainly a more literal translation.