Spheroid distance to sphere distance

I have

• linestring that is calculated on a spheroid.
• Shpere distance of where the point should be on the linestring
• Distance spheroid / sphare.

On one lib, its all calculated in spheroid (Normal map).
Other lib uses sphare.

Lets say the total distances are:
Spheroid: 76363.06884857068
Sphere: 82238.6290291082
The sphareoidic distance from the start would be 409, I need to get distance from spheres perspective.

Any tips where should I look?