Is there a difference in meaning of these adverbs, or are they interchangeable?
They are by no means interchangeable. : The Republican Party has shamefully used the immigration issue to divide Americans. It is shamefully inaccurate reporting by The Guardian.
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They are by no means interchangeable. "shamefully" is the more common word; it is used when some action or quality brings shame or disgrace on the perpetrator in the eyes of others; e.g.:
The Republican Party has shamefully used the immigration issue to divide Americans.
It is shamefully inaccurate reporting by The Guardian.
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