There are two kinds of conventional light water reactor. In the pressurized water reactor (PWR), the most common, there is indeed an additional heat exchanger b

There are two kinds of conventional light water reactor. In the pressurized water reactor (PWR), the most common, there is indeed an additional heat exchanger between the water in the core and the water that turns to steam. In the boiling water reactor (BWR), the second most common, the slightly radioactive steam from the core goes directly to a turbine. https://en.wikipedia.org/wiki/Boiling_water_reactor https://en.wikipedia.org/wiki/Boiling_water_reactor