Basic conceptual/intuitive question on molecular vibrations and rotations.

Could someone please help me get a very basic intuitive understanding of what rotational and vibrational quantum numbers mean? For simplicity, assume a diatomic molecule. For example, does a higher rotational quantum number mean that the molecule is rotating faster? Is the vibration number a measure of the displacement of the atoms from their internuclear distance as they vibrate?
 
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that is their classical analogy yes
 

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