A deep link is a link that lands somewhere specific: not the homepage, but this offer, this member page, this booking. A universal link is Apple's verified form of one, an ordinary HTTPS URL that the merchant's website vouches for, so a phone with the app installed opens the app at the right screen, and every other phone opens the same URL on the web. Android's equivalent is the app link; the behavior is the same idea under a different name.
The web fallback is the load-bearing part. Because a universal link is just a URL, it never dead-ends: the member without the app, or on the other platform, still arrives somewhere useful. That is what makes it the right link type for anything a program puts in front of members, and why a plain app-scheme link, which fails without the app, has largely retired.
Around a wallet pass, deep links do the connecting. Featured actions on a pass face take universal links, so a tap on "offers" lands in the app for members who have it and on the web for the rest. A campaign message can link straight to what it announces. A pass's back fields can carry links, and an App Clip launches from one. Even a save link is a cousin: a URL that lands somewhere specific, in that case a pass into a wallet.
The discipline is the same as with any link: deep links should point at destinations that survive without the app and without a login where possible, because the member who taps is often the one with neither. A program that assumes the happy path in its links quietly loses everyone else.