The usual distinction is between power de facto and de jure.
Power de facto
De facto power is power without any legitimacy or authority. It is simply the ability to achieve objectives despite any resistance. Max Weber offered a definition of power that is essentially similar to this :
Power [Macht] is the probability that one actor within a social relationship will be in a position to carry out his own will despite resistance, regardless of the basis on which this probability rests. (Max Weber in A.M. Henderson and Talcott Parsons, ed., The Theory of Social and Economic Organization, New York: Oxford University Press, 1947, 152.)
There is no rightfulness in such power as such. It could be imposed by a dictatorship or military occupation.
Power de jure
This is rightful or legitimate power. It is or may be every bit as effective as de facto power but it is a moral power with the legitimate entitlement to issue commands and, in doing this, to put others under obligations to act in certain ways. It is closely connected with the idea of *authority'.
Weber : A.M. Henderson and Talcott Parsons, ed., The Theory of Social and Economic Organization, New York: Oxford University Press, 1947.
Jonathan Perry, 'Authority and Harm', Oxford Studies in Political Philosophy, 3, Oxford : OUP, 2017, 252.