In reply to KAUSHIK BHATTACHARJEE.

Any two symmetric distributions (with finite moments) can be made to have the same mean, variance, and skewness. If you choose a symmetric family that asymptotically approaches the normal distribution, you can get the kurtosis to agree as closely as you wish. For example,
the normal distribution and the t distribution with DF >= 605 have the same mean, variance, and skewness. The kurtosis agrees to two decimal places.