Are there any difference between the FFT magnitude of a signal and average FFT magnitudes of the signal broken into multiple frames? Suppose I calculate the FFT of a 5 seconds sound wave. If I'm only interested in the FFT magnitudes across frequencies, I should obtain the same result if I segmented the sound wave into five 1-second frames, obtain the FFT magnitude for each, and taking the average of the magnitude across the frequencies?

Calculating the FFT across a longer signal would allows for smaller frequency resolution, assuming sampling rate is constant.

Does averaging across the frames offer advantages in reducing white noise in the signal? Or does it not matter in that one would get the same result with a long FFT? When might one uses the average magnitudes across frames?

Thanks
You would consider sectioning the overall data into smaller FFT frames for the possible reasons:


you are interested to know that for certain durations of time (length of ye FFT sections) which frequencies were active
there are not enough hardware cycles or resources to carry out a bigger FFT


If you are only interested in knowing what frquencies were ever present in the signal in it's entire duration and you have computation resources to carry out bigger FFTs then yes, you can carry out the FFT of the entire signal itslef. The bigger the sample size of signal duration in time domain over which the FFT is taken the better the resolution in frequency.

For the case you mention you would need to average out by 5 the result of the bigger FFT