No, first cousin twice removed is NOT the same as third cousin. That is why there are two different terms.
Your first cousin twice removed is either the grandchild of your first cousin or the first cousin of one of your grandparents. Which it is depends on which of you is in the generation closest to your common ancestor.
Your third cousin is the great grandchild of one of your great great uncles or great great aunts. Another way to describe your third cousin is the great grandchild of one of the siblings of one of your great grandparents.
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