This is a very interesting question! In order to give a correct answer, we need to discuss some theoretical concepts about conductivity, resistivity and the methods applied for their measurement.

The conductivity is by definition, the reciprocal of the resistivity. It has been found by a number of investigators that the electrical conductivity of hydrocarbon liquids is not a true constant but may vary. It's therefore usual to speak of a "rest conductivity", which is the intrinsic property, and an effective conductivity, which depends on the conditions.

https://books.google.co.ve/books?id=73M6aqqy-uUC&pg=PA1168&l...

Another definition of "rest conductivity" is the electrical conductivity at the initial instant of current measurement after a dc voltage is impressed between electrodes. That definition implies in itself that the conductivity of the solution will vary if a dc voltage is applied. That's why in order to measure this variable accurately, its necessary to use an ac voltage between the electrodes of the conductimeter.

http://docencia.udea.edu.co/cen/QuimicaAnaliticaII/pdf_files...

So, rest conductivity would be the intrinsic property or capacity of a material to conduct electricity, without taking into account external influences; effective conductivity is the result of adding some other external conditions, like for example the variations produced by the measuring device, the temperature of the solution, etc.