Polyatomic ions are just ions that have more than one atom present in them. The only ions not polyatomic would be like H+, Ca 2+, Cl-, Na+, etc which are known as monoatomic. Polyatomic ions would be like ClO3-, OH-, etc. Polyatomic is pretty simple, don't overthink it.
Polyprotic acids are a specific type of acid that have the ability to donate more than one proton. Note the root "prot" in "polyprotic", implying protons. Examples of this would be like what Ad2b mentioned, H3PO4 and H2SO4 (don't think KMnO4 is polyprotic though, has no protons). H3PO4 is polyprotic because it has 3 protons, and can donate 1, 2 or even all three of them to form H2PO4-, HPO4 2-, and PO4 3- respectively.
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Polyatomic vs Polyprotic
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