1.
You use ~ in order to indicate that it does not matter which of the possible alternatives happens or is chosen.
Israel offers automatic citizenship to all Jews who want it, whatever colour they are and ~ language they speak.
= whatever
DET: DET sing-n
•
Whichever is also a conjunction.
We will gladly exchange your goods, or refund your money, ~ you prefer.
= whatever
CONJ
2.
You use ~ to specify which of a number of possibilities is the right one or the one you mean.
...learning to relax by ~ method suits you best.
DET
•
Whichever is also a conjunction.
Fishing is from 6 am to dusk or 10.30pm, ~ is sooner...
CONJ