As defined, influence is a kind of power, and rightly so, firstly because the power to make someone do something if one desires often depends on and involves influence, i.e. what one can make the other believe, and secondly because all forms of social power much depend on influence and ideology.

It also should be noted that in modern society very much money is invested to gain influence, not only in politics and religion, but also in economic markets: Extra-ordinarily large sums of money are spend on advertisements, that not only are attempts to lure people into buying things by false promises and silly associations, but also have a strong tendency to trivialize public debate, and reduce it to the equivalent of sound bytes, slogans, and poses, and to create an average public whose ends in life are largely the having of goods that advertisments lured them into believing is essential for their personal happiness or well-being.

For more on the logic of influence see: Power.