If you have wondered why EDS, EDX, and EDSX seem to be used interchangeably, that is because there is no difference in these terms.
EDS, EDX, and EDXS refer to the same technique: Energy Dispersive X-Ray Spectroscopy.
The most popular name for this technique is EDS, followed by EDX. In my experience, EDS tends to be more popular in the US, while EDX is more popular in Europe.
EDS is a technique usually performed inside a scanning electron microscope (SEM). In EDS, electrons bombard a sample, which emits x-rays. These x-rays are related to the valence electron energy of each atom, so the characteristic energy is unique for each atom. By measuring these x-rays, EDS can calculate the atomic composition of a sample.
Generally speaking, EDS is the most-convenient way to determine the elemental makeup of a material. However, the technique does not have great precision, and it tends to be especially inaccurate when trying to quantify light elements like carbon.
This page is just a definition. If you would like to know more about techniques related to SEM, check out this full article.