I am just wondering what the difference is for these three points of contacts -agent/manager/publicist? I am just looking to get in touch and send a message to the artist to get back to me for work related reasons. Which medium would be best suited for this purpose?
"Send a messages to the artist [for work related reasons]". You would need to be more specific by what you mean. Representation aren't messengers, so if you want to get in touch with the artist directly this isn't the route.
But to answer your question as far as the differences between agent, manager, and publicist, here is a video that does a good job of explaining the differences:
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