Websphere MQ is a software that uses the AMQ(Asynchronous messaging protocol). You can achieve asynchronous messaging between your applications via Websphere MQ, which will make your infrastructure loosely coupled(Applications can keep working even though other applications are down in the infrastructure).
However with the MQ, we need to create your own program using the Websphere MQ API for message transformations. IIB/WMB allows you to create programs very easily and a lot faster.
MQ is providing you the infrastructure for messaging: queues and topic.
IBM Integration Bus (formerly known as WebSphere Message Broker) allows you to apply the common EAI patterns, e.g. Routing, Transformation.