There is code duplication detection and code duplication detection

Many software solutions feature the detection of duplicated source code. Indeed, this is one cornerstone of software analysis and measurement:
It is easy to understand the value of dealing with duplicated code: avoiding the propagation of bugs and evolutions in all copies of the faulty piece of code, promoting reuse, and avoiding an unnecessarily large code base (especially when maintenance outsourcing is billed by the line of code).
Now that everyone is convinced of the importance of such capabilities, lets dive deeper into how to do it. There are various solutions and not all are equal.
Can the difference be explained without looking at an algorithm or cryptic formulas? Let’s try.