A BLEP is a type of Maximum Likelihood Estimator (MLE) that uses only the first derivative of the log-likelihood function. This makes it more efficient than other MLEs, but it can also lead to biased estimates.
An MLEM is a type of Maximum Likelihood Estimator that uses both the first and second derivatives of the log-likelihood function. This makes it more accurate than a BLEP, but it is also more computationally intensive.