Kosher salt is not the "sea salt" that we commonly know, though all salt at some time or another is thought to have originated in the sea.
Both kosher salt and table salt comes from salt mines which have deposits left from prehistoric seawater . Water is squirted onto the salt mine and the salt dissolves into a brine. The brine is then dried. The difference between kosher salt and table salt is in how the brine is processed. Table salt has small square crystals, while kosher salt has larger, flatter, flakier crystals.
Sea salt is harvested from evaporated sea water. There are many different types to choose from, different places of origin, different sizes of crystals and different processing methods.
Kosher salt is called that because it's used in the koshering of meat. In the supermarket it comes in boxes and isn't much more expensive than table salt. Some sea salts can be very expensive and hard to find because it's hand harvested.