I know of lots of studies of implementation that focus on a time
frame past the time of adoption. That means that dissemination of
an innovation occurs, some potential adopters in fact adopt, and
then some of those in fact implement. And we then may study that
time frame of implementation.
Most work in implementation science that I currently see,
however, is something different. It is the study of implementation
prior to the attempt to disseminate an innovation. This is the
study of what study site implementers do with an innovation, for
the objective of understanding quality of implementation, degree of
fidelity, and robustness of an innovation as implemented at
multiple sites. Very often, this is not implementation as a result
of a voluntary adoption decision, but rather implementation as a
result of a site opting in to being part of a study so that
external validity of the innovation can be assessed. It's an
important, prior step along the path toward understanding if an
innovation should then be broadly disseminated so that subsequent
diffusion outcome variables such as adoption and implementation and
sustainability can be studied under real-world conditions.
I expect that those researchers who use the term mean both
"stage 1" implementation and "stage 2" implementation both when
they refer to implementation science. But rarely do they clarify
this processual distinction.