ActiveMQ is a pure JMS play. It lets you implement queues or topics and write listeners or subscribers to respond to queue events.
Mule and ServiceMix are open source ESB (enterprise service bus). An ESB has capabilities beyond JMS: queuing is key, but so are transformation, routing, logging, security, etc.
Apache Camel is an implementation of the patterns in Enterprise Integration Patterns. It uses JMS and other ideas to put the ideas from that book into place.
JMS is fundamental to the other technologies, like JDBC is the foundation for Hibernate, iBatis, etc.
JMS is a spec. ActiveMQ is a particular implementation of it. Camel might be using ActiveMQ, but I'm not certain. I doubt that it's using either Mule or ServiceMix. You can tell by downloading it and looking at the JAR dependencies.
I just did exactly that - no ServiceMix, Mule, or ActiveMQ JARs in Camel. It does use Spring, Lucene, and other technologies.