Front-end developer needs to know:

HTML5, CSS3, JavaScript, jQuery
at least one of the front-end JS frameworks/libraries - Angular, Ember, knockout and React,...
at least one of the UI libraries - Semantic UI, Bootstrap, Foundation, Polymer,...
front-end tools - Gulp, Grunt, Bower
One of the CSS preprocessors - LESS, SASS, Stylus
One of the JS preprocessors - CoffeeScript, TypeScript, LiveScript

Back-end developer needs to know:

Basic HTML, CSS, JavaScript
One of the back-end languages - PHP, Python, Ruby,...
One of the back-end frameworks - PHP (Symfony, Laravel, Nette, Zend, CodeIgniter,...), Ruby (Ruby on Rails), Python (django), JavaScript (Node.js, Express.js, Total.js, Sails.js, Meteor.js)
One of the databases - MySQL, MongoDB, PostgreSQL, MariaDB,...

Full-stack developer needs to know:

All of the above (front-end + back-end)
Meteor.js or MEAN stack.