Islamic Law on "retaliation"

Islamic law devalues the lives of non-Muslims by saying that ['Umdat al-Salik o1.1-01.2]:

Retaliation is obligatory...against anyone who kills a human being purely intentionally and without right.

That means, someone who commits murder must be punished. However:

not subject to retaliation is a Muslim for killing a non-Muslim.

That means that there is no penalty for a Muslim who kills a non-Muslim.

However, in some cases, the injury or death of a non-Muslim may be literally paid off with money, with the perpetrator making a payment to the victim or his family. In that case ['Umdat al-Salik o4.9]:

the indemnity paid for a Jew or Christian is one-third of the indemnity paid for a Muslim. The indemnity paid of a Zoroastrian is one-fifteenth of that a Muslim.