Who are "those whose hearts are to be reconciled," and what is the difference between them and the proselytizing methods of Christians?

Those "whose hearts are to be reconciled" (Al-Mu'allafatu Qulubuhum) are of two types: disbelievers whose conversion to Islam is hoped for, and Muslims whose steadfastness is hoped for. Disbelievers are given from zakat according to the Maliki and Hanbali schools, but not according to the Hanafi and Shafi'i schools. As for Muslims, they are given according to the Maliki, Shafi'i, and Hanbali schools. The Hanafis hold that "those whose hearts are to be reconciled" should not be given anything at present, whether they are disbelievers or Muslims, due to the strength of Islam. If a Muslim is given, it is because they are poor, not because their heart is to be reconciled. Reconciling hearts is about bringing people out of disbelief into Islam, which is the opposite of proselytization (Christianization) that brings people from light into darkness.