core-js is the more common of the two in our index: it runs on 17,920 websites against 1,352 for Select2, and 692 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.
Select2 is a jQuery based replacement for select boxes. It supports searching, remote data sets, and infinite scrolling of results.
692 sites run both core-js and Select2. That is 51% of the sites using Select2, 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.