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When to use generalized estimating equations vs. mixed effects models?

I have a dataset from collected by cluster randomized sampling, I did a logistic regression on this dataset assuming that the dataset is collected by simple random sampling. Now I realize that it may not be appropriate to use simple logistic regression and I am thinking of re-analyzing it.

I am come across two terms: "Multi-level modelling" and "Generalized Estimating Equation". I am using the LEMMA online self-learning resources to learn Multi-level modelling and I haven't read anything about Generalized Estimating Equation yet.

I wonder if two are completely different things? Looks like both can handle cluster randomzied sampled data, but I don't have the details. Can anyone tell me a bit more about the two methods?

Please feel free to comment if further information is needed. Thanks.



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