core-js is the more common of the two in our index: it runs on 18,544 websites against 6,332 for jQuery Migrate, and 3,007 sites use both. Counts come from real scans, not vendor claims.
core-js is a modular standard library for JavaScript, with polyfills for cutting-edge ECMAScript features.
Query Migrate is a javascript library that allows you to preserve the compatibility of your jQuery code developed for versions of jQuery older than 1.9.
3,007 sites run both core-js and jQuery Migrate. That is 47% of the sites using jQuery Migrate, the smaller of the two.
Want to know which one a particular site uses? Look it up and see its whole stack, or compare two sites side by side.