What is the difference between compensation (diyah) and theft (sariqah) when it comes to the hand?

Ibn al-Qayyim said: 

The fact that the hand may be cut off for stealing one-quarter
of a dinar but the diyah (compensation) for the hand [in cases of injury
etc.] may be 500 dinars serves a great interest, and there is a great
deal of wisdom behind this. It serves to take precautions concerning
two things, people’s wealth and people’s limbs. Cutting off the hand
in the case of theft of a quarter of a dinar is to protect people’s
wealth. Making the diyah for injury to the hand 500 dinars is to protect
and preserve people’s limbs. One of the heretics raised this question
and mentioned it in two verses of poetry, saying: 

“A hand receives five hundred dinars’ compensation, so
why can it be chopped off for one-quarter of a dinar?

This is a contradiction we can only keep quiet about,
and we seek the protection of our Lord from disgrace.” 

One of the fuqahaa’ answered him by saying that the hand
is precious so long as it is honest, but when it becomes dishonest it
becomes worthless. And the poet mentioned it by saying: 

“A hand receives five hundred dinars’ compensation, so
why can it be chopped off for one-quarter of a dinar?

Protection against physical aggression makes the hand
precious, but the hand becomes worthless when it becomes dishonest.” 

And it was narrated that al-Shaafa’i responded by saying
in verse: 

“There is aggression against the hand, therefore it is
precious, but here the hand is the wrongdoer, so it becomes insignificant
in the sight of the Creator.”