Business Process Model and Notation (BPMN) is a graphical notation for specifying business processes in a business process diagram (BPD). This can make processes understandable by all business users.
It was previously (until BPMN 2.0) known as Business Process Modeling Notation. Business Process Management Initiative (BPMI) developed BPMN, which has been maintained by the Object Management Group (OMG) since the two organizations merged in 2005. As of January 2011, the current version of BPMN is 2.0.
The official BPMN website can be found here.
Unified Modeling Language (UML) is a standardized, general-purpose modeling language in the field of software engineering.
UML includes a set of graphic notation techniques to create visual models of object-oriented software-intensive systems.
UML was developed in the 1990s and adopted by OMG in 1997. In 2000 UML was accepted by the International Organization for Standardization (ISO) as industry standard for modeling software-intensive systems. The current version of UML is 2.4.1 published by the OMG in August 2011.
The official UML website can be found here.
The only formal relationship between UML and BPMN is that both open standards are maintained by the OMG.
Besides, both are standardized graphical notations which enable business process modeling in the following manner: (1) BPMN is dedicated for business processes modeling; (2) UML has 14 types of diagrams, where UML activity diagrams are suited for business process modeling.
The focal difference between UML and BPMN is that UML is object-oriented, whilst BPMN takes a process-oriented approach, more suitable within a business process domain.
Thus, BPMN is becoming the leader and de-facto standard in business process modeling.