I would say that simultaneous refers to two things happening at the same moment or instant of time, e.g. the flashbulbs went off simultaneously, and concurrent refers to two things happening together over a period of time, e.g. the photographers worked concurrently.
Latin simul 'together, at the same time'. (According to the A-H dictionary, the -taneous is a misanalysis of instantaneous.) This reminds me of the sameness of coincidence and synchronicity.
On a trip in the USA middle-west I noticed many small grocery stores bearing signs labelling them CONVENIENT STORE ..... (the "s" phoneme of "convenience" has melded with that of "store.")
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I see a slight difference, and I think neveu as articulated it. How about concomitant? I've always loved that word. I see that closer to concurrent than simultaneous is.