To me, a main motivation for examining this question from @jrmolle2 is not just how these words are defined in the field but a) how it is practiced and b) how it is perceived by those connected-but-outside the field.
The practice bit seems to be what @clysy and @awkates are referencing to address - not answer, right? - the question, which is probably more productive.
As for how the words are perceived by those outside-yet-connected to The Field(s), I can’t say I know with any real certainty. I suspect that, while they both are formal, assessment might be seen as more so - maybe more operationalized, more structured and tightly framed.
But that’s all based on my teaching and ethnology background and my view that assessment is a type of eval, like @clysy noted. I think I agree with @awkates, too, as long as the assumption of objectivity of assessment is abandoned and that we accept that values are just less apparent in assessment - they are surely there!