Explain the difference between Turing Complete and Turing Equivalence
A system is Turing-complete if it is at least as powerful as Turing machines.
A system is Turing-equivalent if it is exactly as powerful as Turing machines.
An example of a Turing-complete system which is not Turing equivalent is Turing machines with oracle access to an oracle for the halting problem.
One can come up with one additional definition to complete the picture: a system is effective if it is at most as powerful as Turing machines, that is, if every function computed by the system is computable by a Turing machine.