There is almost no connection beteen Java bean and enterprise java bean. Why i used the term "almost" is because the similarity that java bean and ejb have can be found between any two non related classes.
Similarity between Java Bean and EJB:
Both Java Bean and EJB are specification as well as a framework of APIs. Thats it, no similarity other than this.
Difference between Java Bean and EJB:
Basic difference lies between the set of features that they are supposed to support (as i said earlier Java Bean and EJB both provide specification also). Java Bean class is supposed to support component introspection, properties, events and persistence. Component developed according to this specification is called beans. From a developers perspective, a bean is a java class object that encapsulates data in the form of instance variables. These variables are "properties" of the bean. The class also provides getter and setter methods for each variable to access and mutate these properties. A typical java bean class looks like below:
Now let us come to enterprise Java bean. For large enterprise applicatins in a distributed environment we need several issues to be taken care. Like RMI, Load balancing, transparent failover, backend integrations, transaction, security etc etc to name a few. Can you imagince the effort it will take if you write these services yourself. For this reason we have servers that provide these services (better call middleware services) as readymade component. We call these servers as Application server(e.g. IBM Websphere, BEA Weblogic server etc). However these Application servers are supposed to follow the specifications of EJB. Then only the EJB API will be able to talk to these servers and take advantage of the services provided by them. Thus EJB is a component framework that simplifies the process of building enterprise class distributed applications in Java. Now you can appreciate how large is the scope of EJB as compated to java beab (infact there is no comparison). Obviously EJB requires Application server and they are deployable components which is not true for java bean. You don't require application server to make use of java bean.
Bottomline is that the only similarity between a Java Bean and Enterprise Java Bean is there name!