All planes are built using plans for the most part. Scratch does not mean design, design does not mean build. Design and build are two separate things, if you keep them separate it makes everything very easy to understand. I noticed as with most people that push these definitions, they never once mention design.

Design - when you design something, you can design something and not build it. If I was to substitute your definition of scratch in this case I would say I scratched that plan, it make no sense.

Built from Scratch - You built something collecting all of your own materials and parts, this says nothing about who designed the plane it is describing the build.

Designed and Built from Scratch - You designed the plane and collected all of your own materials and built it.

Designed and Built from a kit - You designed it but you built it from a kit assembled for you. Using your definition I would say I scratch kit built that plane.

You don't build plans you build from plans. Plans building makes no sense.

Scratch building is the process of building a scale model "from scratch", ie. from raw materials, rather than building it from a commercial kit, kitbashing or buying it pre-assembled.

Just remember scratch building, it is a process of building, not designing.