The distinction isn't very clear. As you say J2ee is just a collection of libraries, of which Spring web services happen to use a subset of.Servlets/JAX-RS off the top of my head.
Of course Spring doesn't leverage ALL of J2ee but I wouldn't except anything to use all J2ee. There is a lot there.
Said mostly in humor (from long suffering):
The distinction between J2EE and Spring is pretty simple. EJB is a data persistence obfuscation library, whereas Spring's DI/IoC "framework" is an exception (stack trace) obfuscation library.