The distinction seems to be different expected outcome for the subject To "assay" is to engage in an "investigative (analytic) procedure" upon some thing [0].

The distinction seems to be different expected outcome for the subject To "assay" is to engage in an "investigative (analytic) procedure" upon some thing [0]. To "essay" (je vais essayer) is an attempt to achieve a specific thing. The former seems more like an exploration without initial expectations, like a fact finding, focus group, or initial prototype. [0] https://en.wikipedia.org/wiki/Assay https://en.wikipedia.org/wiki/Assay