How to deal with seams
a. There is no seam. We've finessed the seam so thoroughly, you can't even tell. This doctor knows everything about the situation as seen by the last doctor, no need to worry about the handoff. You can't tell where one part of the railing ends and the other begins. Your place in the queue and your records and your status are so clear to the next agent that it won't matter a bit to you that there was a switch.
b. There is a seam. That was one color, this is a different one. That was yesterday, this is today. She was your last teacher, I'm your new teacher.
As you might have guessed, the problematic area is where you try to hide a seam, and you fail.
Seams are a promise, an opportunity, a fresh start. Own them or make them invisible.
A seam can be used metaphorically to describe any sort of discontinuity. In the first case, a patient is transferred from one doctor to another: there is a discontinuity in treatment. In the second case it refers to a change in teachers.
The general idea of the extract is that the two ways of dealing with a discontinuity or change are either to make the impact of the change as small as possible (make the seam invisible) or to present the change as a fresh start and be clear that things will be different after the change has taken place.