Yes, both saltwater and freshwater fish actively drink water. However, the amount they consume depends on the type of environment in which they live.
The habitat of freshwater fish is must less salty than their bodies, causing water to enter their tissues from the surroundings by osmosis. Thus, they need only actively drink a small amount of water to live. Saltwater fish, on the other hand, have bodies that are much less salty than their surroundings. Water, then, tends to leach out of their bodies. They must actively drink more water to live. To rid themselves of the excess salt, they excrete it through special cells in their gills.