A mobile wallet stores payment cards on a phone so it can pay by contactless tap. Apple Pay and Google Wallet are common examples, and they pay over NFC.
The longer version
A mobile wallet holds a person's cards on their phone and lets the phone stand in for the plastic. To pay, the wallet presents a card at a reader over NFC, the same short range tap a contactless card uses. Apple Pay and Google Wallet are widely used examples of NFC wallets.
The wallet improves on a physical card mainly by keeping the real card number off the terminal and behind a device unlock. What it does not change is the gesture. The phone still has to come out and meet the reader, within the few centimetres NFC needs.
Proximity payment addresses the gesture rather than the card store. A wallet still expects the phone to be presented, while a presence based method recognizes the payer without a tap and routes the transaction through a server. The two ideas sit at different layers: where the credential lives, versus how the payer is recognized.
The Parousya method
A mobile wallet answers where a card is stored. The Parousya method answers how the payer is recognized, by presence rather than a tap, so it addresses a different step than the wallet does.