The new Google Wallet looks pretty much like Venmo to me. Send or receive money to friends, cash out to the bank, done with it. The old Google Wallet is being rebranded Android Pay, perhaps to distance itself slightly from Google and maybe let some Amazonians in on the action.
The split and current duplication of names (Google Wallet and Google Wallet (New)) are sure to cause confusion, but that tends to be the way of the Google these days. It looks like they wanted a unifying app to do all things commerce, and then realized that portions were going to compete with certain manufacturers and carriers, so yanked it out.
Whatever the case, the new Google Wallet is for paying friends and family, the old Google Wallet will be changing its name to Android Pay.
Based on the reviews, it appears people are not reading that this is a separate app that only sends money to friends and family as there are a lot of complaints about gift cards.
You can download Google Wallet (New) from Google Play for paying friends and family, or download Google Wallet for tap and pay.
