When I install "web tools platform" plugins in Eclipse I have a new type of project I can create, called "dynamic web project". In such project I can add JSF facet and then use it to make JSF application. But when I install "jboss tools" plugins I have a project type called just "JSF project". What's the difference between both types of projects? Why have jboss tools people created their own type of JSF project?
Eclipse plugins are created to achieve some commonly used/desired configurations at much ease. As you said, you can create a Dynamic Web Prject and then perform couple of steps to convert/support JSF. JSF project is created with those required configuration already done for you.
Same example you can apply even between, a simple project(created though New -> General->Project option) and Dynamic Web Project i.e. you may create a simple project, create files/folders, update the class path etc manually and achieve the same which is directly available through Dynamic Web Project option. These plug-ins/options help you avoid several manual steps to reach a commonly desired functionality. JSF project is no exception.