My earlier answer depended on dictionaries' definitions too much. I mean I use the language, I should know what the function of 就 in different context. In practical sense, at the root, 就 as an adverb has three basic meanings, and they can extend to more meanings with different components, for example, 就座, 就業, 就地, 就緒 and 就捕 are all unique terms that have 就 as a component, that doesn't mean 就 has the meaning of " take the seat, get a job, on the spot, already complete and be captured.
1.then; right away
2.only; just
3.near; close to
Without clear context, the following phrase can be interpreted differently:
有錢就買車- when I have money, then I would buy a car
(就= 1.then; immediately)
有錢就買車- whenever I have money, I only use it to buy car
(就= 2. only; just)
有錢就買車 have money and soon will buy a car.
(就=3. Near; close to; soon)
To avoid confusion, we have to make the context more clear, .
等我有錢就去買車- when I have money, then I would buy a car
(就= 1.then; immediately)
我一有錢就只知道買車- whenever I have money, I only use it to buy car
(就= 2. only; just)
我有錢,就快買車了- I have money and soon will buy a car.
(就=3. Near; close to; soon)
as for 才, it too carries the meanings of "only; just"
the context of 这就是台湾, 这才是台湾 gave room for different interpretations. 这 could mean "这里(here)" or "这样(this way/like this)"
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According to some dictionaries. 就 has 7 meanings as an adverb, 6 as a verb, 3 as a preposition, and 2 as a conjunction.
You can check it out at: http://www.cantonese.sheik.co.uk/dictionary/characters/808/
In 这就是台湾,就 is an adverb (就 [3] [adv] exactly; precisely; definitely )
- 这就是台湾 = This precisely, is Taiwan.
才 as an adverb is simpler, it means "only", only then or "just"
- 这才是台湾 = Only this, is Taiwan.
As for your example sentences:
1a. 你怎么想我就不在乎呢。 As for how you think, I definitely don't care. (就 [3] [adv] exactly; precisely; definitely )
1b. 你怎么想我才不在乎呢。As for how you think, I just don't care.
2a. 两个人就能办好。Just two people can finish it. (就 [4] [adv] only; merely; just)
2b. 两个人才能办好。 Only (having) two people can finish it
3a. 就是他。 It definitely is him.
3b. 才是他。 Only then, is him.
4a. 就是够了。 Forthwith is enough (就 [1] [adv] at once; forthwith; right away )
4b. 才是够了。Only then is enough
Respond to comments:
才 = "only then" in 2b. it is an adverb for 能 - (才能= only then, can)
In 1b, 才 = " just". It is an adjective for 我- (我才 = if it is just me / concerning just me, I don't care).
You can tell 才 is the adjective "just" for the noun when it is followed by a negative statement denoted by 不 or 没
我不认识你= I don't know you
我(才)不认识你= (as far as I am concerned) I don't know you / I (just) don't know you
我没有那么多钱= I don't have that much money
我(才)没有那么多钱= (as far as I am concerned)
I don't have that much money / I (just) don't have that much money