Brief Answer

A fatwā is a universally applicable religious law concerning a particular issue that is derived from the four sources of Islamic law (the Qur'ān, the sunnah, ijmā (consensus), and aql (the intellect)) using the methodology of ijtihād (juristic interpretation).
A hukm o­n the other hand, is a law issued by a qualified mujtahid (jurist) who is the head of an Islamic government. Such a leader, by keeping in mind the general principles of divine law, the Islamic systems (For every aspect of human life, Islam has put forth a set of universal institutions. Taken together, these institutions, in all their aspects, form a structure or “system,” which works towards the objectives that are based o­n Islamic principles. Thus, the “Islamic economic system” is the set of universal institutions applying to the aspects of economics), and prevailing conditions, issues a hukm (legal ruling) for all people, a specific contingency, or an individual.
From the divine perspective, obedience of both a fatwā and a hukm is obligatory. The o­nly difference in this regard is that a fatwā is o­nly legally binding o­n the mujtahid who issues it and his muqallid (one who imitates his rulings), while the hukm is binding o­n all groups or individuals enumerated in the hukm.

Detailed Answer

When a mujtahid derives a legal ruling concerning a given issue by referring to the sources of Islamic law (the Qur'ān, the sunnah, ijmā (consensus), and aql (the intellect)) using the methodology of ijtihād (juristic interpretation), the ruling which he ascertains is called a fatwā. Thus, a fatwā is a universally applicable religious law concerning a particular issue. Imam Khumaynī referred to these methods as the “traditional jurisprudence.”
However, when the mujtahid takes into account the general principles of divine law, the specific system in place in his country, and prevailing conditions, and issues a legal ruling for all people, a specific contingency, or an individual, such a ruling is called a hukm. In this way, a hukm, while taking into account general Islamic principles, values, and goals, also looks to the specific conditions of a people. Therefore, such a ruling remains in place as long as those conditions prevail.
From the divine perspective, obedience of both a fatwā and a hukm is obligatory. Islamic laws are, thus, divided into two categories: “divine laws,” which refer to practical religious laws or “fatwā,” and “authoritative laws,” which pertain to the orders or “hukm” issued by the leader. The o­nly difference in this regard is that a fatwā is o­nly legally binding o­n the mujtahid who issues it and his muqallid (one who imitates his rulings), while the hukm is binding o­n all groups or individuals enumerated in the hukm.