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Here's how Google explained it in May:
"Today, we’re letting web merchants know that in six months, Google Checkout will be retired as we transition to Google Wallet — a platform that enables merchants to meet the demands of a multi-screen world where consumers shop in-stores, at their desks and on their mobile devices."
So both are online payment processing services -- until November, when Google Checkout, which debuted in 2006, is retired. It sounds as if Google Wallet is much more geared to today's mobile shopping environment.