Apache OpenEJB and Apache TomEE are born from the same project and community. They differ in two major ways, only one of them technical:

Effectively, TomEE is a superset of OpenEJB. They share the same code and TomEE grew out of OpenEJB.

Tomcat TomEE TomEE JAXRS TomEE+ TomEE PluME OpenEJB
Java Servlets
Java ServerPages (JSP)
Java ServerFaces (JSF)
Java Transaction API (JTA)
Java Persistence API (JPA)
Java Contexts and Dependency Injection (CDI)
Java Authentication and Authorization Service (JAAS)
Java Authorization Contract for Containers (JACC)
JavaMail API
Bean Validation
Enterprise JavaBeans
Java API for RESTful Web Services (JAX-RS)
Java API for XML Web Services (JAX-WS)
Java EE Connector Architecture
Java Messaging Service (JMS)
EclipseLink
Mojarra