Your vocabulary is a bit confusing.
Coordinate transformations usually referes to transforming the underlying datum,
not reprojecting the coordinates.
In this case, your datums are the same (WGS 1984),
so no transformation should be required, just a projection.
Conceptually, features are projected, not from the earth, but from a generalized figure (a globe)
The datum defines the globe.
Using differently defined globes (datums) can lead to very different locations for features,
so transformation from one dataum to another can be significant.
It is true that a projection 'transforms' the globe onto a plane
(sometimes with intermediate steps such as a developable surface (a cylinder or cone)
or with rotaions or skews...), but we usually refer to it as projecting rather than transforming.
How far apart are the locations that should be coincident?
In what direction do they lay?
and most important:
What exactly did you do to each of the (geographic coordinate) data sets?
(tools and parameters, please)