The issue: your project, say wp-calypso, assumes a certain version of eslint as specified in package.json. Maybe the project's .eslintrc.js file is incompatible with other versions of Eslint. Meanwhile, you are often expected to run eslint as a global command on your system. That, however, becomes a problem once you have different projects working with different versions of all sorts of Node-based global tools (e.g. eslint, babel, etc.).
The solution is to use npm-which, which returns the path for a certain program that is local to your project. That is:
cd wp-calypso
npm-which eslint # outputs something like $MY_PROJECT_DIR/node_modules/.bin/eslint
# compare with