You are right:

1) J2EE is container based and Application server provides vital services like DB connection pooling, transaction management etc.

2) J2EE application are mainly web application or ejb application .war or .ear or web services they require application server to run. web application can also run on web server like tomcat.

3) On broader term J2EE is collection of technology e.g. Servlet, JSP and EJB for building http based application.