In short; surface tension is the property of a liquid in contact with a gas phase (usually air). Interfacial tension, on the other hand, is a property between any two substances. It can be liquid-liquid, liquid-solid or solid-air.
Surface tension and interfacial tension are usually denoted by the symbol σ and are measured by force per unit length. Its SI unit is millinewtons per meter (mN/m), which is equivalent to the commonly used cgs unit, dynes/centimeter (dynes/cm).
To understand where surface tension and interfacial tension come from, we need to understand two more terms: cohesion and adhesion.
Cohesion is the interaction between similar molecules
Cohesion is the attractive force between molecules that are similar to each other. Cohesion is the intermolecular force that causes a liquid to resist separation. In water, for example, there are strong cohesive forces, hydrogen bonds, that allow rain to fall in droplets rather than fog.
The cohesion between molecules is responsible for the surface tension. Alternatively, the imbalance of these forces arises from the fact that there are fewer neighboring molecules on the surface than most in the liquid.
The cohesive forces on solids are so strong that solids do not stick to the material they touch. On the other hand, liquids like water also have adhesive forces that allow them to interact with other liquids and solids.

Adhesion is the interaction between different molecules
Adhesion is an interaction between different molecules. Adhesion is caused by forces acting between two substrates, such as mechanical and electrostatic forces. Adhesion forces come into play when two immiscible liquids come into contact. Adhesion is also important when liquids come into contact with solids.
Surface tension and interfacial tension are important in many industrial applications
Surface tension and interfacial tension are important in many industrial applications. For example, surface tension can be measured when the critical micelle concentration needs to be determined. On the other hand, interfacial tension is an important parameter for emulsion stability.
