The fitdist function uses maximum likelihood. The exceptions are the normal and lognormal distributions. For the normal distribution, the mle of sigma^2 is 1/n times the sum of squared deviations from the mean. But using the factor 1/(n-1) instead is very common, because it makes the variance estimate unbiased. That's what fitdist uses. It does the analogous thing for lognormal.
The mle function uses maximum likelihood even in those two cases.
