Google Shopping[1] is a search engine for products - it lets you search for a product and then compare prices across different retailers etc.
Google Checkout/Wallet[2] is a payment services provider, somewhat like PayPal or Stripe. Most popular use is probably for buying things from the google play store. It's been renamed to Google Wallet[3], and can no longer be used for accepting payments for physical goods.
1: http://www.google.com/shopping