Re: z-transform and DTFT
The principal difference between the Z and the discrete time fourier transform is that, the DTFT is a derived of the Z transform, because, in the Z transform, Z means a complex number (Ae^(Θ)) with any magnitude and any phase angle, but in the DTFT, this complex number is restricted to an only magnitude, A must be only one (1), it's means that the complex number is e^(Θ).
Another difference is that the analysis of the Z transform is valid for all types of signal (periodic, increasing, decreasing, etc), but the DTFT its valid only for signal that has finite energy and the completely periodic signals.
You can find another more complete explication in the SIGNAL AN SYSTEM book.