In my experience, we have drawn the line at what already exists vs. what doesn’t exist already. For example, let’s say we are integrating reporting for a department. We can ask, “What reports do you currently rely on?” to both teams. Then we make sure that the reports for the new merged team includes the information that is currently critical to run their business. If, however, during those conversations one or both teams say, “we currently use X report, but we really would really like to have a Y report too,” the Y report would be considered an optimization project that would be out of scope for the integration. Creating a new type of report that doesn’t already exist would take time and resources away from the integration efforts. Another way of summing this up would be to differentiate between the things that are critical to have vs. nice to have.
I think there is a 3rd term to consider and that is operational. A business needs to function as usual for its day to day activities, combine said activities, and then maximize the value of these activities. Here is an example with an ERP.
Start: Company A and Company B have different ERPs
Operational: A bridge is built between the two ERPs until they can migrate to one
Integration: Company A and B migrate to one ERP
Optimization: NewCo (Company A and B) use other modules within this ERP and clean up erroneous data