Load cells are usually equivalent to pressure sensors, force sensors, and/or pressure sensors. Although there is a lot of overlap between these categories, from load cell manufacturers
Technically speaking, they do not have the same membership set.
A sensor is any device that can sense physical phenomena and react accordingly. The output may be readable or not meaningful.
By definition, a transducer always converts its sensed input into a readable, meaningful output. Most transducers convert physical phenomena into interpretable electrical signals. However, there are some exceptions (for example, pressure sensors that produce light output instead of electrical output).
A load cell is generally understood as a pressure sensor that only produces an electrical output.
In addition, there is a slight difference between the phenomena actually measured by the pressure sensor and the load cell. The pressure sensor specifically measures pressure, which is defined as the force exerted on a set surface or area (measured in Pascals, psi, etc.). On the other hand, the double shear beam load cell usually directly measures the force (in Newtons) without referring to a specific area.