I'm not sure if I understand the difference between Turing Complete and Turing Equivalent programming languages.
A computational system that can compute every Turing-computable function is called Turing-complete (or Turing-powerful).
A Turing-complete system is called Turing-equivalent if every function it can compute is also Turing-computable; i.e., it computes precisely the same class of functions as do Turing machines.
I'm not sure if I understand the difference between these two terminologies properly and what "Turing-computable" means. So for example if I have a programming language $X$, it is Turing complete if it can do any and everything that a Turing Machine can do? And it $X$ ends up being Turing complete and it can be shown that all of the functions that it computes are Turing computable, then $X$ is also Turing equivalent?