Question about aliasing As far as I understand, you can have two different continuous-time signals with the same discrete-time frequency spectrum after they are sampled and it may be possible these shifted replicas in the discrete frequency domain do not overlap with each other. In textbooks aliasing is associated with overlapping of shifted replicas. is the case I described a case of aliasing?
What you describe is indeed aliasing. If there are frequency components above half the sampling frequency then they will be folded back to the interval $[0,f_s/2]$. This folding back is called aliasing, no matter whether these aliased components overlap with other parts of the signal spectrum or not.
Note that you can also use aliasing to your advantage if you're careful that no overlap occurs. An example is bandpass sampling, where you deliberately choose a sampling frequency that is much smaller than twice the highest signal frequency.