The different symptoms are listed in the User Support Wiki
People have different ways of using the terms, but strictly I believe they should be as follows:
Imbalance is a feeling of unsteadiness. Sometimes one leg feels heavier than the other or less sure. You feel off-balance, lob-sided.
Dizziness is a fuzzy non-specific feeling of lack of surety of where you are in space. It is not a spinning sensation.
Spinning is as its name suggests, a feeling of going round and round.
Vertigo can be a spinning sensation, but also a fast, anxious, falling sensation or quick ‘whoosh’ feeling.
Then you can get all sorts of other sensations, like you say rocking/swaying, see the link above.