The vocabulary now used for this dispute is philosophical before it is theological. J. M. E. McTaggart's 1908 argument distinguished an "A-series" description of events as past, present and future from a "B-series" description of them as merely earlier and later, and framed the question of whether time's passage is real or a feature of how events are ordered. Presentism and eternalism are answers to that question rather than terms either school of theology coined for itself.
A third position sits between them and is easy to miss if the choice is presented as binary. The "growing block" view holds that the past and present are real and the future is not yet, so that reality itself accumulates as time passes. It shares eternalism's commitment to a real past and presentism's commitment to an open future, and some theologians attracted to both a solid past and genuine divine risk-taking have found it a more workable model than either pure position.
How a body treats divine eternity tracks this dispute closely, and traditions have not settled on one answer. Classical theism, in its Thomist and Reformed forms, favours an eternalist or timeless framing in which God's single act of knowing spans all moments without succession. Open theism explicitly rejects that framing as incompatible with a genuinely undetermined future, and adopts a temporal, presentist or growing-block God who comes to know events as they occur rather than knowing them changelessly in advance. Process theology goes further, making God's own experience temporal and cumulative by definition.