Sam's Club, which is owned and operated by its parent company Walmart, sells its own brand of gasoline, so the brand is Sam's Club. Walmart gas stations sell Murphy brand gasoline. There might be instances in which a Sam's Club warehouse might sell Murphy gasoline or vice versa.
Sam's Club endeavors to keep prices as low as possible for its customers. By not selling a major gasoline brand, Sam's Club can theoretically save customers money. Sam's Club gas pumps require purchasers to swipe a Sam's Club membership card, so those who want to save money by filling up at Sam's Club gas stations have to pay for a Sam's Club membership.