Power VS Authority? What is the difference?

Power can be seen as various forms of constraint on human action, but also as that which makes action possible, although in a limited scope. Much of this debate is related to the works of the French philosopher Michel Foucault (1926-1984), who, following the Italian political philosopher Niccolò Machiavelli (1469-1527), sees power as "a complex strategic situation in a given society [social setting]". Being deeply structural, his concept involves both constraint and enablement. For a purely enabling (and voluntaristic) concept of power see the works of Anthony Giddens.
The imposition need not involve coercion (force or threat of force). Thus "power" in the sociological sense subsumes both physical power and political power, including many of the types listed at power. In some ways it more closely resembles what everyday English-speakers call "influence", although some authors (like D. Wrong) make a sharp distinction between influence as a more general concept, and power as intended influence.
More generally, one could define "power" as the more or less unilateral ability (real or perceived) or potential to bring about significant change, usually in people’s lives, through the actions of oneself or of others.
The exercise of power seems endemic to humans as social and gregarious beings.

"The phenomena called authority is at once more ancient and more fundamental than the phenomena called state; the natural ascendancy of some men over others is the principle of all human organizations and all human advances."Bertrand de Jouvenel
In politics, authority (Latin auctoritas, used in Roman law as opposed to potestas and imperium) is often used interchangeably with the term "power". However, their meanings differ. "Power" refers to the ability to achieve certain ends, 'authority' refers to the legitimacy, justification and right to exercise that power. For example whilst a mob has the power to punish a criminal, such as through lynching, only the courts have the authority to order capital punishment.
Since the emergence of social sciences, authority has been a subject of research in a variety of empirical settings; the family (parental authority), small groups (informal authority of leadership), intermediate organizations such as schools, churches, armies,industrial and bureaucracies (organizational and bureaucratic authority) and society wide or inclusive organizations ranging from the most primitive tribal society to the modern nation-state and intermediate organization (political authority).
The jurisdiction of political authority, the location of sovereignty, the balancing of freedom and authority, the requirements of political obligations have been core questions for political philosophers from Plato and Aristotle to the present.