Can anyone simplify how GLS estimation is different from FGLS estimation? I understand that the covariance matrix is estimated in FGLS using OLS. What are some other differences?
No other differences. A lot of consequences though, due to this tiny little gap between "known" and "estimated".
Like, mostly unknown finite sample performance, loss of asymptotic properties if heteroskedasticity is misspecified... this is the reason why, ever since a consistent estimator of the coefficient-estimator's covariance matrix has emerged (the White-, heteroskedasticity-robust one), $FGLS$ is much less used than before.