Does FFT on two samples from the same audio but with a very small sampling offset return the same results?
Fourier transforms possess a form of (in magnitude) shift-invariance, also called time-invariance, or shift property (see Properties of the Fourier Transform-shift properties): &quot;a shift in time corresponds to a phase rotation in the frequency domain&quot;:
$$F\{x(t−t_0)\}=\exp(−j2πft_0)F\{x(t)\}\,.$$
This property of the continuous Fourier transform has analogues in its discretized versions. So many techniques to compensate for shifts or synchronize signals are based on this property. I'll name a few ones: cross-correlation, time-delay estimation, generalized cross-correlation (GCC), fractional delay filters. They can give you initial pointers.
In Matlab, functions like finddelay or alignsignals can be used.