A turbo back will consist of a sport downpipe (normally of a greater bore to the standard system), a sports catalytic convertor (less cells which allows for more air to pass through), and then also the cat-back system, which is basically some more metal piping, the backbox and the tailpipes.
Cat back will provide increased noise but little power increase / if any.
Turbo-back will sometimes provide slightyyyy more noise than a cat back, but performance gains will be apparent also!