they have many common features. but how the difference?
MOM allow asynchronous while SOA does not, this is the only difference?
Answer
SOA, Service Oriented Architecture, is an architecture that defines how to structure access to business information between different applications. In a nutshell, usually, one application needs something done with a piece of information (may it be an orderfile or anything else) that application has a need. Another application may be able to do the corresponding processing of that piece of information, hence it has a capability. The first application then Consumes the Service of the second application, which Provides the Service (no matter the underlying technology, which can be anything such as JMS, HTTP/SOAP, HTTP/REST, EMail, FTP, etc.). To make this work, a Contract between the first application and the Service has to be defined which clears such things out as Message Format (XSD or similar), Protocol (HTTP/SOAP? JMS?) etc.
MOM, Message Oriented Middleware, on the other hand is just a family of software/middleware platforms. They are actual implementations, and not a high-level concept like SOA. They can be used to implement a SOA architecture, an Event Driven architecture or other architectures. Usually, MOM enriches a set of applications with asynchronous messaging where a MOM server stores and forwards the messages. Often things such as transactions, guranteed delivery, fail-over, loose coupling and load balancing are built into MOM implementations. Examples of MOM are IBM WebSphere MQ, Apache ActiveMQ, RabbitMQ, JBoss HornetQ, etc.