这就是台湾，这才是台湾. Cracking the 就 again
A lot of people are trying to explain 就 vs 才 with english equivalent terms, but that makes it very confusing when it can be explained with simple logic statements, and it is crucial to understand the reasoning behind all these cases:


  X就Y -> Y if X
  
  X才Y -> Y if and only if X


The difference is that when using 就, X is not the only condition that Y can happen, while with 才 Y happens [if and only if] X happens. Basic example:


  下雨的話(X)地就會濕(Y)
  
  The floor will get wet (Y) [if] it rains (X)
  
  下雨的話(X)地才會濕(Y)
  
  The floor will get wet (Y) [if and only] if it rains (X)


Mutated form of 就 vs 才:


  你怎么想我(X)就不在乎呢(Y)。
  
  I wouldn't care (Y) [if] however you think of me (X)
  
  你怎么想我(X)才不在乎呢(Y)。
  
  I wouldn't care (Y) [if and only if] however you think of me (X)


But wait a second, how does that make any sense?

You see, "I wouldn't care" is the result of "however you think of me", the action. By using 就 you are simply stating that you wouldn't care how he thinks of you. But in some cases that's not powerful enough, and only in chinese that you can deliver that kind of tone: you want to tell the other person you don't care so much that "however you think of me" is the ONLY thing that you don't care about, and you care about everything else.


  两个人(X)就能办好(Y)。
  
  It can be done (Y) [with] two people (X).
  
  两个人(X)才能办好(Y)。
  
  It can be done (Y) [with and only with] two people (X). 
  
  (Note that this can imply strictly 2 persons, or 2 or more people) 


The following is harder to explain:


  就是他。
  
  That is (simply) him
  
  才是他。
  
  That is (the real) him


You would use 就是他 when you see someone doing something that he normally does. 


  那就是菲尔普斯(Y)，又贏獎牌了(X)
  
  That is Michael Phelps (Y), winning yet another medal (X)
  
  ([Because] of winning another swimming medal, he has to be Michael Phelps)


But then let's say Michael Phelps had been on a losing streak for the past few of games, and he has finally gotten another medal.


  那才是我知道的菲尔普斯！
  
  Oh yeah that is the true Michael Phelps that I know of!
  
  (This signifies that it is the real Michael Phelps [because and ONLY because] he has won again and he is known for winning. It wasn't him when he wasn't winning. You would use this form when you want to confirm that something is finally back in shape or back to where it used to be.)


Finally, quite straight forward:


  就是够了
  
  That is enough.
  
  才是够了。
  
  That is just enough.