Undecided questions
what the difference between (Head of state , president)

Correction: What is the difference between "Head of State" and "President"?

Sometimes the Head of State and the President can refer to the same individual as in the United States, but the Head of State as a title reserved for the person(s) who hold the highest position in a nation differs for other forms of government. Wikipedia goes into it in far more detail: http://en.wikipedia.org/wiki/Head_of_state

In the United States, the president is the head of state. I don't know about other countries.

Note:

When using the word "president," it is not capitalized unless it is used as a proper noun. For example: "George Washington was the first president of the United States." In this case, "president" is not a proper noun, it is just a noun. But when the word "president" is used as a proper noun, it is capitalized. For example: "The current occupant of the White House is President Barack Obama."