In my (positively prejudiced!) explorations and practices of Mere Christianity - I have noted some sharp differences in the understanding of what happens immediately after death.
Here are brief accounts, necessarily simplistic:
1. The Protestant view seems to be that it is at or immediately after the moment of death when the soul is allocated to salvation or judgment.
After that point, nothing can be done to change its ultimate destiny - the final judgment may not be known at this exact point, but it is predestined.
The domain of salvation is restricted to the span of human life.The boundary between time and eternity is the moment of death, and the state of the soul at the moment of transition is therefore permanent and unalterable.
So prayers for the salvation of the dead are at best futile, and at worst a kind of blasphemy - because assuming that human intervention can affect what is between God and the soul of the departed.
2. The Eastern Orthodox view seems to be that there is a period of forty days following death during which the soul is evaluated - and during which prayers of the still living may affect this evaluation - then the soul is allocated by the first judgment (awaiting the final judgment).
The domain of salvation extends beyond human life - but is essentially time limited; after which the soul enters eternity, and does not change.
Consequently, prayers for the dead are regarded as necessary, and especially immediately after death.
(The salvific effectuality of later prayers is not ruled-out, but is much less clear.)
3. The Roman Catholic view seems to be complex, and I am not sure I have grasped it. After death, most Heaven bound souls require purgatory before Heaven.
There is a strong emphasis on the effectuality of prayers for the dead, but - unlike Orthodoxy - the timing of such prayers is not critical, and prayer may be retroactive in its effects.
So, the soul is evaluated and purged, and during this process in linear time, the prayers of the living - past, present and future - are all brought to bear on the situation.
The domain of linear time seems to extend beyond the moment of death and to the end of purgatory, at least - which is not a fixed length of time, and perhaps linear time after death is not mapped onto linear time before death; after which the soul enters eternity and does not change.
4. In Mormonism, death is a positive experience of transition to a potentially higher level of exaltation, and necessary to move to the next stage.
Any soul that will consent to be saved (and which has not implicitly rejected salvation by severe and unrepented sin) is evaluated and allocated to its proper place in a multi-level Heaven (or several Heavens); where the possibility of progression upward is open-ended.
In Mormon metaphysics, there is only linear and irreversible time, eternity is simply open ended linear sequential time; so there is no possibility of retroactive prayer being effective - but prayer for the dead may be effective in the sense that there is an 'ongoing process' that may be affected.
As the last comment describes, the differences are partly theological and ultimately metaphysical - concerned with time and the nature of eternity.
In some accounts the soul can change its salvific state after death, in other accounts the soul is fixed at death.
And these differences have a large influence on the nature of Christian practice, and account for many of the most obvious differences between denominations.
For example, when I worship at a Protestant Anglican Church we never pray for the dead; while at Anglo-Catholic Churches we spend a lot of time in prayer for the dead, even in short Masses - and that difference is within a single denomination.