The simple answer is that a fault is a mistake in stroke execution, a mistake made in the manner of hitting the ball with the mallet. An error is a mistake that concerns the nature of the stroke, even if it is executed correctly.
The errors are best understood by asking a sequence of questions:
If the question was really "why are some errors forgiven while others, including faults, are not forgiven", the answer is that "serious" errors (i.e. Law 25, 26 and 27(d)) are fatal errors and the turn ends, "trivial" errors (Law 27(i) - balls misplaced in minor ways) are treated leniently as a matter of pragmatism and "middling" errors (i.e. Laws 27(e) to (h)) are treated leniently as a matter of policy.
The game would be unplayable if the striker's turn was ended if he played whenever a ball could be shown to be a millimetre out of position. That is why I describe the policy to treat such errors leniently as pragmatic.
There is a case for making "middling" errors fatal and this was suggested in 2000 but rejected by all four countries. The example usually given is that it would be unfair if a striker took off to two distant balls and hit one of them but was unsure which ball was roqueted and made the wrong choice. Another is where the striker does not notice that his ball has glanced a ball in a long take-off.
Speaking personally, I believe the error laws would be simplified if these errors were made fatal and the striker could protect himself by the simple expedient of checking with his opponent before playing the next stroke. However, I do not expect a change in policy any time soon.
Faults apply directly to lawful strokes and have always been fatal in that the turn ends. They also apply to strokes which constitute non-fatal errors via Law 27(j).