Why do require and fs.existSync use different relative paths

The path you use for require is relative to the file in which you call require (so relative to routes/index.js); the path you use for fs.existsSync() (and the other fs functions) is relative to the current working directory (which is the directory that was current when you started node, provided that your app doesn't execute fs.chdir to change it).

As for the reason of this difference, I can only guess, but require is a mechanism for which some 'extra' logic w.r.t. finding other modules makes sense. It should also not be influenced by runtime changes in the application, like the aforementioned fs.chdir.

Since the relative path to a file is relative to process.cwd(), as mentioned in this link. You can use path.resolve to resolve the path relative to the location as below:

const path = require('path');

const desiredPath = path.resolve(__dirname, './file-location');
console.log(fs.existsSync(desiredPath)); // returns true if exists