A wallet pass on a watch is the same pass, on a smaller screen, without the phone leaving the pocket. For a member it is the fastest identification route there is: raise the wrist, hold it to the reader, done.
On Apple Watch the pairing is automatic. Passes added to Apple Wallet on the iPhone sync to the paired watch, and the wallet app on the watch shows them with their barcode and fields. NFC identification works from the watch through Apple VAS, with auto-presentment bringing up the matching pass as the wrist meets the reader, so a program that works on iPhone works on the watch without extra configuration. Live updates arrive the same way they do on the phone.
Google Wallet on Wear OS is newer and carries a subset of what the phone holds. Loyalty, gift and other pass types are shown on the watch with their barcodes; NFC presentment of passes via Google Smart Tap depends on the watch and pass type, so it is worth verifying on the devices a program's members actually wear rather than assuming parity with the phone.
Two practical notes for programs. Barcodes on a watch are small and the screen is curved, so a QR code scans more reliably than a long linear barcode; QR and barcode identification should be tested on a watch at the till, not just on a phone. And because the watch shows only the pass's fields, a pass whose key information lives in an image will lose it on the wrist; keep the balance and the member's status in fields.