Doppler is the change of pitch or frequency due to the source or destination moving. Aliasing is the generation of components when two signals go through a non linear process, which mimic the one of interest, for instance if you sampled a 1 KHZ with a 1KHZ sampling frequency, it would give the same results as sampling a 2 KHZ frequency or a 3 KHZ frequency.
Frank
The two effects have in common that they can alter the apparent frequency of a signal, but their origins are completely different. As Frank said, Doppler comes from relative movement, and aliasing comes from sampling.
Regards