Internally they build dependency graphs which map every modules your projects need and generate one or module bundles.
Rollup is another module bundler that can output both library and application, has default support to ES Modules and famous for tree shaking from early days. Rollup also has plugin system to customize its behavior like transpiling code before bundling or finding third-party modules in our node_modules folder.
Browserify is a tool for bundling Node packages for the browser, happens to work for browser-based apps pretending to be Node packages. The module system that browserify uses is the same as node, so packages published to npm that were originally intended for use in node but not browsers will work just fine in the browser too.