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Can stratified sampling be non-random, random or both?

I'm revising Biology but I think this is more of a Stats issue.

Stratifed sampling comes under the heading non-random in the OCR A Bio textbook, but I would have thought it is in part random and non-random. If your strata are different sizes and you're taking a proportionate number of your total samples from each, then going back to the original population each observation is not equally likely to be selected, hence I can see the logic behind calling it a non-random technique. But then within each stratum you generate your samples randomly and need a complete sampling frame? Different sources are saying different things and I am SO CONFUSED lol

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