They are two different problems that usually go together. Salinity is an excess of soluble salts: the plant has water around it but cannot drink it, because the salt retains it. Sodicity is excess sodium in the exchange complex: the soil disperses, loses structure, becomes impermeable and becomes waterlogged.
The practical effect is the same: the list of what can be planted is narrowed. In mild degrees it is managed with tolerant species; in severe degrees the land is left for grazing, and in the extreme it is a salt flat without agricultural use.