As @Aristos has mentioned, you can look into PayPal and/or Amazon Checkout.
Both of them provide alternative/3rd party checkout services - which is what Google Checkout is (was after November 2013).
Braintree is a payment processor and is very different from Google Checkout and any other checkout services - they offer credit card processing services (just like Authorize.net, Paypal Payflow, etc.). You will need to have/apply for a merchant account and comply with PCI DSS requirements when using such services (although they have services that minimize your PCI DSS work).
Google Wallet for Online Commerce (aka "Instant Buy") is a "layer" on top of such - which is the Google product/service that will "assume" the role of the "payment flow" (I hesitate to call it a "payment service" as it's really not) for merchants selling physical goods. It will work with (in fact require) your existing payment processor.
Wallet for Digital (aka "In-App Payment"), as the name implies, is the digital (product/service) counterpart of "Instant Buy". This is still a 3rd party checkout service - meaning it's still Google that handles the credit card processing (just like Checkout does/did). But it's primarily for digital merchants (selling digital products).