Very different--the legally protected freedom of religion found in "Golden Age" Andalusia, or Al-Andalus, was unique in contemporary medieval Europe. In the early 700s, when the Islamic Empire's expeditionary forces first arrived in Andalusia, they had the full support of the Umayyad dynasty in Damascus. But by midcentury, the Abbasids in Baghdad had taken over the Empire. The last surviving Ummayad heir, Abd Ar-Rahman I, escaped the purge of his relatives and declared himself the true Emperor in Cordoba. But since he commanded only a few small garrisons there, he didn't even have enough troops to control Andalusia, much less threaten the Abbasid Emperor four thousand miles away.

Instead, Abd Ar-Rahman I was able to win local supporters by promising religious tolerance for Andalusian Christians and Jews of any sect. By the 900s, during the reign of Abd Ar-Rahman III, religious freedom for all monotheists was codified into law, without the restrictions on non-Muslims typical in the Empire proper (extra taxes, no government posts, no bearing witness in court). Cordoba grew almost as large as Constantinople, and the Abbasids even officially recognized Andalusia as a legitimate independent country.

Andalusia's power peaked in the 1000s; then it fractured into warring city-states and went into decline, ultimately being conquered by the Catholic kingdoms of Castile and Aragon to form Spain in the late 1400s. Cordoba stayed relatively prosperous nearly up until the end, but in general the successor city-states, stocking their militaries with imported mercenaries, lacked the religious tolerance that was a distinguishing feature of united Andalusia.

(Sources: Islamic and Christian Spain, Thomas Glick; The Buried Mirror, Carlos Fuentes.)

Different but not that different. The Abbasid may have more of a different varieties, since Sufism(Mystical Islam), Shi'a, all 4 school of Islam were very popular there and the controversial Mu`tazila.

While Caliphate of Cordoba was called Caliphate officially 929 before that they were Emirate(756-929), think of it a King calling himself an Emperor but with a religious hint. They were more inclined towards lesser know school of Islam and afterwards transitioned to the Maliki School of Islam (one of the fours), other than that they were cool and lived in much more of a pluralistic society. Their successors were much harsher to their non-Muslim subjects.