So I guess TDS and Total Conductivity share similarities but they are certainly not the same.
TDS and electrical conductivity
The term TDS describes all solids (usually mineral salts) that are dissolved in water. The TDS and the electrical conductivity are in a close connection. The more salts are dissolved in the water, the higher is the value of the electric conductivity. The majority of solids, which remain in the water after a sand filter, are dissolved ions. Sodium chloride for example is found in water as Na+ and Cl-. High purity water that contains in the ideal case only H2O without salts or minerals has a very low electrical conductivity. The water temperature affects the electric conductivity so that its value increases from 2 up to 3 % per 1 degree Celsius.
http://www.lenntech.com/tds-ec_engels.htm