My understanding is that Apple Pay enables the payment, but Apple does not collect or retain any data such as to whom you paid how much. Here's what Apple's iOS Security Guide say:
"Apple Pay is also designed to protect the user’s personal information. Apple Pay doesn’t collect any transaction information that can be tied back to the user. Payment transactions are between the user, the merchant, and the card issuer."
Two different animals. Apple Pay lets consumers purchase goods from a merchant. Google's offering in that space is Android Pay. Google Wallet is more similar to Venmo in that it's only for peer to peer transactions.
"Apple Pay is also designed to protect the user’s personal information. Apple Pay doesn’t collect any transaction information that can be tied back to the user. Payment transactions are between the user, the merchant, and the card issuer."
https://www.apple.com/business/docs/iOS_Security_Guide.pdf