Are the words "coincident" and "simultaneous" considered synonymous? Else, please explain the difference In discussions, experimental and thought-experimental descriptions (especially concerning the Theory of Relativity) the words "coincident" and "simultaneous" appear, notably for instance in the foundational literature as:

All our well-substantiated space-time propositions amount to the determination of space-time coincidences [such as] encounters between two or more recognizable material points.

and

We thus require a definition of simultaneity such that this definition supplies us with the method by means of which, in the present case, he can decide by experiment whether or not both the lightning strokes occurred simultaneously.

Are these two words (at least for these purposes) considered to be synonymous; referring to the very same notion? 
Or else: Please clarify the difference between the corresponding two distinct notions.
 A: "Coincident" is defined in the Google online dictionary as (1) "occurring together in space OR time" (emphasis mine), and (2) "in agreement or harmony".
"Simultaneous" is defined in the same dictionary as "occurring, operating, or done at the same time".  (This begs the question: "Whose time?")  Unfortunately, this dictionary lists "coincident" as a synonym of "simultaneous".  I do not think this is a precise synonym.  It should be avoided.
Used in the context of relativity, "coincident" might be considered a way of describing events which may or may not exhibit simultaneity.
The two examples of usage that you show in your question, illustrate this difference in meaning.  A coincidence includes simultaneity, but may also include an event that is not simultaneous.
A: In the context of Relativty, the adjective "coincident" characterizes all that which belongs together ("at once") to only one event without any temporal or spatial or light-like separation; i.e. indications (of any participant at this one event) or occurences (as far as they are understood to be contained within this one event).
In contrast, the adjective "simultaneous" characterizes (possible) pairwise relations between suitable elements (indications, occurances) of certain (necessarily space-like) separate events.
Taken together, Einstein's statements quoted in the OP imply that the notion of "simultaneity" must be defined in terms of determinations of (or conditions on) of who or what had been coincident, or not been coincident.
Accordingly, the words "coincident" and "simultaneous" should denote strictly distinct notions. The occasional use (e.g. in the foundational literature, especially in some of Einstein's own writings) of the word "simultaneous" where the word "coincident" is fitting instead seems due to negligence.
