To answer if a salt is formed between the reaction of a base and an acid, we need to remember that, if we react a strong acid and a strong base, such as HCl and NaOH, two products will be formed: the appropriate salt and water.
In the example above, we can write the reaction as:
HCl + NaOH -> NaCl + H2O
where a strong acid and a strong base react to form a salt (NaCl) and water (H2O).
Thus, we can say that, yes, a salt is formed when an acid and a base react between each other.