Is soap (potassium soap/sodium soap) a salt? Explain on the basis of chemical structure.

Yes a soap is a salt

Explanation:

The process of soap production is called saponification. Saponification is the hydrolysis of fats and oils with a caustic alkali such as NaOH or KOH to yield the corresponding sodium or potassium salt of the fatty acid and propane 1,2,3-triol.

Recall that organic salts are compounds of the sort RCOO^-M^+ (such as RCOO^-Na^+). A soap is of the same RCOO^-Na^+ (or K^+) structure indicating that it is a salt where R is the alkyl chain of the fatty acid.