No. Salt and sodium are not the same thing.
"Salt" is the term commonly used for sodium chloride (NaCl) which is table salt. Sodium chloride is just 40% sodium and 60% chloride. One teaspoon of table salt contains 2,325 mg of sodium.
It's important to note that in addition to sodium chloride, sodium shows up in food in other forms including monosodium glutamate (MSG), sodium bicarbonate (baking soda) and sodium nitrate (a preservative) among many others.