I think they are the same in spoken language.
"再" here has no meaning of "again".
However they can be used in different situations.
"吃完飯再來談"
I'll say this before or during eating.
To me, it means "I already know we should talk later".
"吃完飯才來談"
I'll say this after the conversation. To describe when we talk.
Or as an outsider.
Hope it helps.
November 24, 2015
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再, refer to one more time, do it again, one more, two more, three more and continue. 再一次。表示重复或继续,多指未然:再说。
才, refer to just. then ,only just. 现在才明白。才用了两元。来了才十天。