Shop Pay is the more common of the two in our index: it runs on 337 websites against 10 for Zip. Counts come from real scans, not vendor claims.
Shop Pay is an accelerated checkout that lets customers save their email address, credit card, and shipping and billing information so they can complete their transaction faster the next time they are directed to the Shopify checkout.
Zip is a payment service that lets you receive your purchase now and spread the total cost over a interest-free payment schedule.
Want to know which one a particular site uses? Look it up and see its whole stack, or compare two sites side by side.