Pipe Fixed/Moving Image/Transform to ImageToImageMetricV4 vs ImageRegistrationMethodV4

Hi all,
I’m working on a registration problem and I am confused how both ImageToImageMetricV4 and ImageRegistrationMethodV4 offer a Set[Initial]Fixed(Moving)Image(Transform) function.

In a typical registration pipeline from most examples, Images and Transforms are set on the registration objects whereas interpolators are set on the metric.
Looking figure 3.9 of the Software Guide, it makes more sense that it is the Metric which uses the Transform and Interpolator to compute its values.
Or are they chained underneath, i.e. the registration objects first applies its transform then queries the metric, which itself applies another transform (identity by default), to compute a final value? That’s what I’m guessing, I might be wrong.