The Hudson River is an estuary: a freshwater river that flows into the ocean, where it mixes with salt water. The degree of mixture between fresh and salt water is called the salinity gradient. On the Hudson, the salinity gradient at a given location can vary considerably depending on factors such as time of year, tidal flow, and precipitation.
It's a different story on the Connecticut River, and no coincidence that Dutch explorers dubbed it the Fresh River; so much water pours through it that the river's waters turn completely fresh little more than a mile inland from Long Island Sound.