The main diffirents between a PWR (pressurised water reactor) and a BWR, (boiling water reactor) both light water reactors, is that the former consist of two coolant cycles, while the latter only consists of one.
The PWR's primary coolant system uses light water as coolant, at a temprature of aprox. 275 degrees C. The coolant remains liquid, despite the high temprature, because of the high pressure (up to 155 BAR) in the reactor vessel.
The primary coolent then heats up the secondairy coolent in the steam generators, wich powers the steam turbine generators.

Boiling water reactors have only one coolant system. The coolant is used both for cooling the fuel rods as well as to be turned into steam for powering the steam turbines.

Both reactors use their coolant water as neutron moderator.
The water slows down the high velocity neutron, allowing them to interact with the fuel rods, allowing the nuclear reaction to be sustained.
Because both reactors use water as a neutron moderator, both systems naturally have a negative temprature coëfficient. This means that as the temprature in the reactor rises, the reactivity of fuel starts to decrease, causing the reactor to power down untill the temprature decreases again. This makes the reactor more stable to controll, as well as help prevent damage to the reactor core due to overheating.
The negative temprature coëfficient can be explained by the expansion of water creating more space between the water molecules, thus decreasing the moderative capabilities of the water, and allowing less neutrons to interract with the fuel.
The biggest advantages of PWR's over BWR's are the following:
-Because of the higher pressure in PWR's the coolants moderative capabilities are naturally higher than that of the BWR. This allows for a smaller reactor vessel for a reactor of the same power. Thus decreasing the reactors size as well as cost.
-By having two seperated coolant systems the PWR prevents radioactive contamination to reach to steam generators, and steam turbines. Therefore these systems will, unlike the BWR, not need radioactive shielding.
Disadvantages when compared to BWR's are:
-Because of the high pressure of the primary coolant, the reactor needs highly strenghtened piping, and vessel construction, as well as increase the consequences of a rupture leading to coolant loss.
-The neutron flux from the reactor can cause the steel from wich the reactor vessel is constructed to become brittle over time, limiting the reactor vessels lifetime.
-The high temprature coolant water with boric acid dissolved into it can cause radioactive corrosion to most metals.