Estimate a new project

API - It's backend's project. It works as an endpoints and usually returns json or XML data. It's often only one part of bigger project. More about API you can read on wikipedia.

WWW - It's a website. Standard web application where the functionalities are not splited on backend and frontend developers. Person who is working on project like this is called Full stack developer.

Mobile - It's mobile application, you can install on your smartphone or tablet. It works on Android, iOS, Windows Phone or other platforms. It might be implemented in the hybrid framework, or native language for each platform. You can choose this type of project when application consuming API but API is created or will be implemented by someone else.

Mobile + API - Mobile and API projects marged together. You should choose this type of project when you are responsible for coding mobile application as well as backend.

Frontend - This type of application usually works on clients side and most of the time is implemented in JS frameworks (AngularJS / ReactJS etc).