I have to say I disagree with /u/amphibiousdog's rather simplistic take on this question. The concept of Zakat appears to have changed and developed over time. There is evidence that in the time of Muhammad that it was a kind of purifying payment in recompense for sin, while by the times of the reforms of Abd al-Malik under the Ummayad Caliphate that it was changed into a compulsory tax.

One result of that understanding that it was a purification penalty paid specifically to Muhamamad was that a number of particularly Bedouin tribes are reported to have stopped paying it after Muhammad's death. This ended up playing a role in the Ridda (Apostasy) Wars after Muhammad's death, where a distinction was drawn between those who had actually apostatized and those who merely refused to pay the Zakat.

As you might imagine, the quasi-obligatory nature of the tax to the Caliphs also had ramifications for Alid supporters who held that the other Rashidun Caliphs were illegitimate.

Nor was it initially only for "people adhering to the Islamic faith." Quran 2:83, for instance, makes clear that Jews were obligated to pay the Zakat.

Understanding the "Jizya" as a tax on non-Muslims is equally simplistic. In a pre-Islamic context it appears that Jizya simply meant poll tax, and that after the conquests it was the tax imposed on the conquered people who, yes, were non-Muslims but who couldn't actually convert to Islam initially. In other words it was indistinguishable from the imperial poll taxes of, in particular, the Sassanians upon whom it might have been modeled. The Jizya as religiously descriminatory tax also appears with Abd al-Malik.

As to the amounts paid, I'd be fascinated to know your source for "usually 2.5% of their annual income." The documentary evidence suggests that there was incredible range of tax arrangements in the early Islamic state.

As Hoyland notes: "By the second half of the eighth century, the island of privilege that the early Arab conquest society had been no longer existed. An average Muslim very likely paid less tax than an average non-Muslim, but it varied according to profession and status, and of course the reality of tax collection was very much more complex than the simple and elegant theories of the lawyers."

See the discussions of Jizya and Zakat in Hoyland's In God's Path, Donner's Muhammad and the Believers and in "On the Origins and Development of the Meaning of zakāt in Early Islam" by Suliman Bashear in Arabica.