The actual story of the salt in the sea and on land is quite a remarkable one. Surprisingly, it involves the chemistry of the atmosphere!
Bascially, there are two questions:
(1) if the rivers are continually washing salt to the sea, why isn't the sea getting saltier and saltier?
(2) why are many salt lakes much saltier than the sea?
There is a third, hidden question:
(3) why are most desert soils quite salty?
We know that when saltwater evaporates, the water becomes vapour, and it leaves the salt behind.
We can easily determine, by measuring salt levels in rivers, that more salt is continually being brought into the ocean.
The salt must therefore be getting recycled somehow. Moving through the land is not a realistic possibility. We know that geological processes move land around, but they are much too slow to keep up with the amount of salt recycling. That leaves moving through the air with the winds as the only possible option for salt recycling.
Salt does not evaporate with ocean water. Instead, it gets into the atmosphere in stormy weather. Choppy waves make splashes. But the splashes are large droplets of water that quickly fall back near where they were made. But waves also make bubbles under the water, When these bubbles come to the surface and burst, they cause absolutely tiny droplets of water to get thrown into the air. These droplets are so small (sub-microscopic) that their natural rate of falling is only a few centimetres per hour. And the speed and form of storm winds can easily carry them very high very quickly. The water content of the tiny droplets can evaporate fully or partly, leaving even smaller particles. The air, all around the world, at all heights, contains some of these tiny salt particles, usually called halites. If it were not for the presence of these halites, it would be very difficult for clouds to form.
There are basically three things that can eventually happen to halites. They can be dry deposited on land. If it rains, they will be washed into rivers and be taken back to the oceans. If not, they will accumulate, and help produce the typical saltiness of a desert soil. They can be deposited directly back into the ocean. No interesting story there. Or they can be incorporated into clouds. They make condensation nuclei, which can allow clouds to grow by adding just one water molecule at a time. If it were not for halites and other nucleating particles, water droplets or ice crystals for clouds could only form if about 1000 water molecules decided to meet at the same place at the same time -- a huge co-incidence.
The eventual fate of these particular halites is to come down with rain or snow when and where the cloud eventually precipitates. And thus they again find their way into rivers and back to the ocean.
Salty inland lakes? Well, lakes of this sort are less subject to the formation of halites, because smaller bodies of water have smaller waves, which produce fewer bubbles when they get choppy. So recycling is much less efficient for these bodies of water, and they accumulate a lot of salt from run-in. Similar story to the salty desert soils.