lecture video 9, lesson 1, week 4, Confidence intervals for proportion

in proportion distribution, we have,

mu or mean = p

and

std = sqrt(p*q/n).
but as i know from central limit theorem,
SE = std/ sqrt(n).
then why I found that SE = sqrt(p*q/n). which is the same as std.

anyone can explain this? for me, following central limit theorem formula,

SE should be equal to sqrt(p

*q/n^2) = sqrt(p*q)/n.

anyone can explain what I miss?