[theory] What is Turing Complete?

As Waylon Flinn said:

Turing Complete means that it is at least as powerful as a Turing Machine.

I believe this is incorrect, a system is Turing complete if it's exactly as powerful as the Turing Machine, i.e. every computation done by the machine can be done by the system, but also every computation done by the system can be done by the Turing machine.