What is the difference between Newton's first & third law? Newton first law states that object stays in fixed state, unless external force is applied.
Newton third law states that: if there is action then there will be opposite & equal reaction. 
So if we apply external force on object nothing but a action, so object moved is nothing but a reaction. So newton first & third law are same?
 A: There is a sense in which the first and third laws are the same, because the are both just saying that momentum is conserved. The first law tells us that the momentum of an isolated object remains constant, and the third law tells us that the net change of momentum in any interaction between two bodies is zero i.e. momentum is conserved.
So both laws can be deduced from the statement that momentum is conserved. These days we would derive this from symmetry principles.
A: Newton's first law says that unless an object is applied a force it will continue its motion with the same velocity (or linear momentum). This law expresses the homogeneity of the Euclidian space: nothing changes from one place in the space to another.
Newton's third law says that if a body A acts on a body B by a force $\vec F$, then the body B acts also on the body A by a force $-\vec F$. What you say "So if we apply external force on object (is) nothing but a action, so object moved is nothing but a reaction", is not correct because the force you name "action" acts on you object - let's call it B - and reaction is a force with which B acts back on the object - let's call it A - that applied the force on B.
Though there is some truth in your idea, in the sense that from the 3rd law one can conclude the following: taking the two objects, A and B as a system, the forces applied by the parts of the system (A and B in our case) on one another, won't change the state of movement of the system as a whole. 
A: 
Newton third law states that: if there is action then there will be opposite & equal reaction.

What you are missing is that the action and reaction forces apply to two different objects. Newton's third law says that if object A exerts a force on object B, then object B must necessarily exert an equal but opposite force on object A.
Just because two forces are equal but opposite does not mean that these forces are third law interaction pairs. For example, consider a book resting on a table. Gravity exerts a downward force on the book and the table exerts an equal but opposite upward force on the book. These are not third law forces. An easy test of whether two forces are third law pairs is to determine whether the two forces act on different bodies. In this example, both forces act on the book, and thus these two forces are not third law action-reaction forces. In this example, the third law reaction to the gravitational force exerted by the Earth on the book is a gravitational force exerted by the book on the Earth. The reaction to the upward normal force exerted by the table on the book is a downward normal force exerted by the book on the table.
