Is the pressure difference induced by the surface tension or is the surface tension the result of the pressure difference?
If one looks up the behavior of liquid at the interface of two media
say water and air-
one can find the two kind of forces operating between molecules in the vicinity of a water molecule at the surface in contact with air.
In the spherical region of influence around the molecule the lower hemisphere is filled up with water and the upper one has air -
thus the forces of cohesion between water molecules give a net cohesive force and the upper hemisphere molecules provide force of adhesion between water and air molecules.
If the force of Cohesion between water molecules is greater than force of adhesion between water and air molecules,
the surface of water exerts a membrane like stretching force to contain the water in its lowest energy state and
that builds up the surface tension forces and its net result is excess pressure inside the liquid than outside -
Hence the forces of cohesion leads to surface tension and consequently surface energy and the difference of pressure gets created
rather than the reverse that pressure differences being instrumental in leading to such curvatures and surface tension effects.