Three distinct claims are routinely confused here, and separating them is the first task.
Determinism is the thesis that every event is necessitated by prior events together with the laws of nature, so that given the past, only one future is possible. Fatalism is the different and older thesis that certain outcomes will occur regardless of what anyone does, that the appointment in Samarra is kept whichever road is taken. Determinism does not entail fatalism: on a determinist account what one does is part of the causal chain and makes a genuine difference to the outcome, whereas fatalism holds that it does not. Free will is the capacity at issue in both.
Hard determinism accepts determinism and concludes that free will, understood as the ability to have done otherwise, does not exist. Some contemporary philosophers and neuroscientists hold it, and the experimental work initiated by Benjamin Libet in the 1980s on neural activity preceding conscious decision is regularly invoked in support and equally regularly disputed on methodological and interpretive grounds.
Fatalism in its ancient and folk forms appears in the Greek Moirai, in Norse wyrd and the Norns, in popular understandings of the Islamic vocabulary of qadar, and in the widespread sense that what is written cannot be evaded. Theologians in most traditions have resisted it, since it makes moral exhortation pointless, but it recurs in popular religion everywhere and is remarkably resistant to correction.
Libertarian free will holds that determinism is false, at least for human choices, and that agents originate actions in a way leaving genuinely open alternatives. It is the position most religious doctrines of accountability appear to require, and its standing difficulty is to explain how an undetermined choice is not simply random, which would make it no freer than a determined one.
Compatibilism holds that free will and determinism are consistent, because what freedom requires is acting according to one's own will without external constraint or compulsion, not that one could have willed otherwise. It was the Stoic position, was developed by Hobbes and Hume, and is the majority view among contemporary academic philosophers by a substantial margin in surveys of the profession. Its critics regard it as changing the subject rather than answering the question.
The religious versions of the debate track these closely. Islamic kalam set the Qadariyya and Mu'tazila against the Jabriyya, with the Ash'ari doctrine of kasb attempting a middle course. Christian theology ran Augustine against Pelagius, Luther against Erasmus on the bondage of the will, and Calvinism against Arminianism, with Molinism as an ingenious attempt at reconciliation. Hindu and Buddhist traditions meet the question through karma, and both insist that karma is not fatalism, the Buddha is recorded as rejecting the doctrine of Makkhali Gosala, who taught that everything is fixed and effort useless, as the most pernicious of all views.