By Java they usually mean J2SE, the standard (base) set of VM and APIs.
J2EE
is the set of all enterprise technologies (servlets, JSPs, EJBs, etc.) that
build on top of the standard edition.
I would add that when someone is asking for java experience, they might be
doing thick client development, most likely swing (or maybe IBM's SWT?).
Another slant is they might even be looking at a jr developer to turn into a
web/n-tier developer.
If they are asking for J2EE, they are most likely looking for someone who
has created web applications (using JSPs and servlets) and very likely want
someone with EJB (Session and/or EJB and/or message driven beans)
experience. And lastly, they are also looking at someone who's intimate
with some type of IDE (Eclipse, JB, etc) and server (Tomcat, WebLogic,
Websphere, JBoss, etc).
I came from the MS world and I would equate it to someone asking for VB
experience or ASP experience. The VB person can write up a program to do
stuff on a computer (thick client), but the ASP person is using VB/VBS to
create a web application using MS Internet Information Server (IIS)
accessing a db (most likely SQL Server) and maybe even MS Transaction Server
too!
Good luck! :>