1) Point-to-Point 2) Publish and Subscribe.
Point-to-Point messaging consists of queues, senders and receivers. A message can be received by only one receiver. Receiver does not have to be active at the time of sending. Receiver gets the message from the queue and sends the acknowledgement to the sender.
Publish-and-Subscribe messaging consist of topics, publishers and subscribers. Consumers subscribe to a particular topic and get the messages of that topic. A message can be received by many subscribers/consumers. An application that subscribes to a topic can only consume messages published after the client has created a subscription and subscriber is active before that time.