When to use the DTFT vs the DFT (and their inverses) in analysis?
DFT and DTFT are obviously similar as they both generate the fourier spectrum of time-discrete signals. However, while the DTFT is defined to process an infinitely long signal (sum from -infinity to infinity), the DFT is defined to process a periodic signal (the periodic part being of finite length).

We know that the number of frequency bins in your spectrum is always equal to the number of samples processed, so this also gives a difference in the spectrums they produce: the DFT spectrum is discrete while the DTFT spectrum is continuous (but both are periodic with respect to the Nyquist frequency).

Since it is impossible to process an infinite number of samples the DTFT is of less importance for actual computational processing; it mainly exists for analytical purposes.

The DFT however, with its finite input vector length, is perfectly suitable for processing. The fact that the input signal is supposed to be an excerpt of a periodic signal however is disregarded most of the time: When you transform a DFT-spectrum back to the time-domain you will get the same signal of wich you calculated the spectrum in the first place.

So while it does not matter for the computations you should note that what you are seeing there is not the actual spectrum of your signal. It is the spectrum of a theoretical signal that you would get if you periodically repeated the input vector.

So I would assume in the literature you were mentioning, every time it is important that the spectrum you're working with is actually the spectrum and disregarding the computation side of things, the author would pick the DTFT.