Difference between the DTFT and DFT
A DFT produces a finite number of results (frequency bins), so the complex result vector can be indexed by 0..(N-1).

A DTFT produces a result over a continuous range of frequencies (more than a finite number of results) so must be specified by a real number as opposed to an integer.

As MBaz says, you can sample the DTFT at a fixed integer number of points.