Surface tension is $S = dU/dA$, or the rate of change of surface energy with respect to area. It is a property of both fluids together. This can be understood by thinking about what happens to a particle near the fluid interface compared to a particle immersed among its own.
On average the immersed particle will be pulled in all directions evenly, whereas the particle at the interface will be attracted toward or away from the interface, depending on the molecular properties of both fluids.
You can imagine fluids with very similar molecules might behave almost as though there was no interface. In fluids with very different molecules, particles might be drawn either more towards their own kind, or more toward the other kind.
The former case is true of water and air, where water is much more attracted to itself that it is to air. It forms a sheet-like interface that supports being deformed into droplets and other complex shapes. By contrast, ethanol is not as strongly attracted to itself, and cannot sustain as much deformation in air.
It is this intuition, based on comparison against a reference fluid, that leads some people to mistake surface tension for a property of an individual substance.