Conversion factor for conductivity of an aqueous solution
I think you have badly confused yourself by mixing the concept of a property of a solution with the units used to express this property.
Total dissolved solids (TDS) is a property of a solution. Theoretically, it can have any units kg/ kg of a solution, part per million, percentage, or whatever you like. However, people have standardized what they mean by TDS is usually mg solids/L of solution or even ppm.
In the same way, EC is electrical conductivity. It is a property of a solution. It can be expressed in units of microSiemens/cm or any multiple of it. EC itself is not a unit.