This paper establishes the Firefly Algorithm (FA) to be a special variant of the conventional Accelerated Particle Swarm Optimization (APSO) technique by suggesting modifications in the movement criteria of the fireflies in case of the simple FA. In order to find the significance of this implication, a well known optimization problem known as the Economic Dispatch problem is computed for multiple test cases. Economic dispatch problem aims to minimize the total fuel cost of a multi-generator power system. In addition, the valve point effect loading is considered for the thermal cost equation in order to make the objective function more non-linear and non-convex in nature. The modified and enhanced FA not only improves its performance as compared to the conventional FA, but also presents enhanced FA as a special case of the APSO algorithm by giving the similar performance parameters as that of APSO. Moreover, a comprehensive statistical analysis based on the results of the independent t-test is presented in order to statistically compare the performance of APSO, FA and enhanced FA. The independent t-test results statistically prove enhanced FA to be a special variant of APSO technique by comparing the mean and the variance of the two algorithms for a particular sample size.