First things first, I’ll acknowledge that there’s no black-and-white answer, and that words will mean different things to different people. But I do experience a difference between authenticity and honesty, in that sometimes the totally authentic reply to something might be “I don’t want to talk about that” or “I don’t feel comfortable sharing more right now.”
All this is against the backdrop of any individuals culture and their own context, social norms, etc. though. I think, actually, it’s less about choosing to be authentic in all ways at all times. One, that’s impossible and two, that might not be your own right decision. But I think it is about getting more in touch with your default, and noticing when a habit of withdrawing is actually doing more harm than good.