It seems Google is now in the process of readying the Google Contacts app to make sending payments to other people easier. This is due to the latest version of the app (version 2.5) having now been spotted including a new 'send money' feature. In spite of the functionality having now been seen, it does seem that the update is rolling out on a slow basis as very few users have been noted with the feature live. Therefore, having the latest version of the Contacts app installed is currently no guarantee of the feature. Even if the feature is live on any particular device, it also seems the use of it is a little limited during this early stage of deployment and will of course require additional steps to have been taken, such as having a payment option set up with Google.
In either case, and once working on a device, the feature itself seems pretty straightforward. A user opens the Contacts app, head to any particular contact and at the top of the individual contact page – where quick action links such as "Call," "Text" and "Video" are located – a new quick action "Send" link will be present, along with a "$" icon (as shown below). Clicking the link launches the interface allowing the user to confirm the recipient and state the amount. Then it appears to be just a matter of hitting the "Send Money" link to complete the transaction.
While this is new to Contacts it is an extension of the same feature available through Android Messages. When the Messages version launched the payment transactions were powered by Google Wallet and while that is still technically the case with the new Contacts implementation, Google Wallet has more recently been rebranded as "Google Pay Send." So in spite of the name difference this is essentially a Google Wallet integration. Wallet's rebranding occurred as part of an even wider rebranding of Google's payment service(s) in general. One which saw the fairly recently launched Android Pay become Google Pay. Resulting in the two more clearly-defined services, Google Pay and Google Pay Send. One for making payments in general and one for paying people directly – including through Android Messages and Contacts.