Definition:
Behavioral models describe the internal dynamic aspects of an information system that supports the business processes in an organization. During analysis, behavioral models describe what the internal logic of the processes is without specifying how the processes are to be implemented. Later, in the design and implementation phases, the detailed design of the operations contained in the object is fully specified.
Use case diagrams are behavior diagrams used to describe a set of actions (use cases) that some system or systems (subject) should or can perform in collaboration with one or more external users of the system (actors) to provide some observable and valuable results to the actors or other stakeholders of the system(s).
Note, that UML 2.4 specification also defines use case diagrams as specialization of class diagrams (which are structure diagrams). Use case diagrams could be considered as a special case of class diagrams where classifiers are restricted to be either actors or use cases and the most used relationship is association.
Activity diagram shows sequence and conditions for coordinating lower-level behaviors, rather than which classifiers own those behaviors. These are commonly called control flow and object flow models.
Behavior diagrams emphasize what must happen in the system being modeled. Since behavior diagrams illustrate the behavior of a system, they are used extensively to describe the functionality of software systems. As an example, the activity diagram describes the business and operational step-by-step activities of the components in a system.
Design and (symbols):
State machine diagram is used for modeling discrete behavior through finite state transitions. In addition to expressing the behavior of a part of the system, state machines can also be used to express the usage protocol of part of a system. These two kinds of state machines are referred to as behavioral state machines and protocol state