There is one other key difference between drugstores and grocery stores: inventory.
Grocery stores usually stock plenty of everything. Drugstores don't have as much space. So you should either go at the beginning of the sale or if a bargain item has sold out, be sure to ask for a rain check.
Drugstores' regular prices are likely to be higher than big box store prices, but if you cherry pick drugstore sales, you can get deals like these:
Ragu pasta sauce: Big box price, $1.76. Drugstore price: $1.66
Raisin Bran: Big box price, $2.98. Drugstore price, $1.99
Starbucks coffee 4-pack: Big box store, $5.48. Drugstore price: $3.99