What is the difference between the way we calculate the margin of error for population proportion and population mean?

The main difference can be directly observed in the formulas used to calculate for the margin of error.

For the population mean, the margin of error would simply be:

MOE = z * s / sqrt(n)
where z is the z-score, s is the standard deviation and n is the number of samples

For the population proportion, the margin of error is:

MOE = z * sqrt[p (1 – p) / n]

where p is the probability of success