No. High Tension lines are literally installed under high tension, mechanical strain, to reduce sag between supports.
They tend to increase together as the higher voltage insulator supports get more and more expensive as the voltage goes up. So the economics of longer spans with corresponding tensions tends to go up with voltage. But water, road and other physicals constraints also justify higher tension and longer span construction.
Well, both. There is a valid term called “electric(al) tension” which means the same thing as electrical potential or voltage.