Is there any difference between un tanto and un poco as both mean "a bit"?
No there is no difference other than "un poco" being a bit more commonly used.
In everyday use both un poco and un tanto could have a number of variations on just meaning "a bit.' It may not follow that both would be used in exactly the same way by native speakers all the time. It is worth looking at the lesson - search on "un tanto / algo" and you will see how "un tanto" has a number of uses that I suspect may not exactly fit with "un poco" though only the teachers or another native speaker could tell you.
Yes, the only difference is the level of formality - un tanto/ algo are both slightly more formal than "un poco". If there is a specific nuance with un tanto/algo, I would say that we tend to use these for sentences that use a bit of irony/sarcasm.
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