Cooling towers are specifically when you don't use river water for cooling.

Your first photo has a large lake in front of it, so clearly they will use that, but the rest don't, they only have the towers.

Nuclear plants almost always use once-through cooling or cooling ponds, but coal plants typically don't, and are unaffected by the heat limits (which are environmental for fish, not technical for power generation).

Edit: Notice how in the diagram you linked there is a river for cooling, but there is no tower? Coal plants will have one or the other, but nuclear uses both, and that's because most of the waste heat from coal goes up the chimney.