mechanical rounout is the distance from probe to surface if there is no vibration of the probe,
electrical runout should better renamed electro-magnetic runout is the measure that is taken by a transducer that uses one of the many possibilities of electro-magnetic distance sensing.
In your situation this is eddy current, so first question: which frequency, which material penetration depth of eddy current to be estimated. Or a swept frequency/distributed frequency sensing?
So the eddy current sees a totally different situation, it is located at some depth below the surface.
Only if the material is very homogeneous - in the electromagnetic sense, that is with respect to electric resistivity and magnetic permeability both with respect to frequency - only then these give nearly the same results as pure geometric measurements. (The latter suffer from surface geometry and radius of measurement tip and dirt).
So if you want to have high accuracy eddy current measurements (very similar to geometric measurements) then avoid any magnetic material at the part to be measured, get the best available electric conductivity, make a heat treatment to relieve stress and finish the surface to a smoothness and planarity better than your measurement accuracy shall be.
And be sure to use a high frequency transducer to have only a small penetration depth.
Or (better) switch over to a capacitive or optical transducer - these have different errors.
Think about oxides on the surface, think about absorbed water, oil and gas, think about scratches and more.
Inside your transducer area there are many hills and valleys of your surface, which mean surface do you want?
Think about filtering these mountains with your transducer geometry and that there may be (likely) some aliasing by repeated measurements being taken.
Measurement is a difficult field of high variety in errors.
Thank you very much for your reply to my question. In my case, it is Bently nevada Vibration monitoring system 3300. The material to be observed is AISI 4140 and so is the material of the shaft of compressor.
Simply put, when you slow roll the shaft on the balancing machine etc there is no unbalance as such, so any reading of shaft "movement" that is observed by the system 3300 is a combination of electrical and mechanical runout. Mechanical being the machining/grinding/bending tolerance at the probe track, surface roughness etc and the electrical being mostly residual magnetism.
This runout may be subtracted from the reading that you get when the shaft is running at speed in order to get the actual "out of balance" displacement.