In due time MoneyGram separated from the Western Union and became an independent brand. MoneyGram's consumers and agents expect reliability and safety and that is precisely what MoneyGram continues to deliver, transaction by transaction. The benefits of money transfers by MoneyGram: simplicity in making up. The Global Funds Transfer segment is the primary segment of MoneyGram, providing money transfer and bill payment services to consumers, who are often unbanked or underbanked.