Static modeling is used to specify structure of the 
objects that exist in the problem domain. These are 
expressed using class, object and USECASE diagrams. 

 Dynamic modeling refers representing the object 
interactions during runtime. It is represented by sequence, 
activity, collaboration and statechart diagrams

Static Model - Time Independent view of the system.
e.g. Class has same number of students in an year.
Static model includes :
CLASS DIAGRAM
OBJECT DIAGRAM
COMPONENT DIAGRAM
DEPLOYMENT DIAGRAM

Dynamic Model - Time dependent view of the system
E.g. ATM can accept card only when it is in ready state. 
ATM cannot read card card when it is in ERROR state. Thus 
state of ATM is a dynamic aspect.
Dynamic Modelling includes
USE-CASE DIAGRAM
INTERACTION DIAGRAM
STATE DIAGRAM
ACTIVITY DIAGRAM

Funtional Model-What happens
Static Model- To whom it happens
Dynamic Model - When it Happens

Static Model refers to the model of system not during 
runtime. This is more structural than behavioral. This 
includes classes and it relationships(Class Diagram), 
Packages etc. For example, the concept of class itself 
static. At runtime there is no concept of Class, Sub class 
etc.

Dynamic model refers to runtime model of the system. This 
includes the concept of Objects, interactions, 
Collaborations, sequences of operations, Activities, state 
changes, memory model etc.