Duplicate your full sized shape and edit the duplicate to to cover smaller area. Remove unwanted stroke and add possibly wanted fill.
In your example case the edited duplicate has a fill, but hasn't a stroke.
For example add 2 new nodes where you want the exact match to stop. You can at these points split the path, delete the unwanted portion, draw a new and join the parts.
As well you can edit the path with the node tool, no need to delete a part. The added nodes are your guards who keep all edits out of the exact match area.
A duplicate (Ctrl+D) was made, colored differently and edited with the node tool
GN = inserted guard nodes (actually only one was inserted, the other was already in a good place in the original shape)
- The edited shape got a fill, its stroke was removed and the shape was sent to the bottom
You may have a bigger shape which has just the wanted edge and you may want to use that edge as the separation line. An example:
The black shape is wanted as whole and the orange shape is used for separation.
Both shapes are duplicated and an intersection is created
The remnants are removed, the intersection is sent to back and colored
I do not recommend to use clipping instead of intersection. It's easy to think that intersection shouldn't be used, because it's destructive. Clipping with a mask (Object > Clip > Set) creates the same looking result, but the clip can be released and the shapes are restored - this is the common thinking.
In Inkscape it's not true. The result really looks the same, but when one releases the clip, the shapes come back differently:
The orange shape (=the clipping mask) has lost its form.
NOTE: I do not know if this is a bug in the software or my system malfunction or do I have wrong software version for my system. I use Inkscape 0.92.2 portable in a 64bit system which can be a wrong selection.