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I'm confused because my lecture notes state that chelate ligands are a subset of polydentate ligands.

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    $\begingroup$ That's true. A chelate ligand is necessarily polydentate, but not vice versa. $\endgroup$
    – Ivan Neretin
    Commented Feb 13, 2019 at 20:29

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A chelating ligand should bind more than once to the same metal atom. Therefore, it must be polydentate. However, a regular polydentate ligand does not have to ligate to the same metal, and therefore, it is not necessarily chelating.

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