Of course there isn't any difference in the Fourier analysis, but there is a difference between spectroscopy and MRI, enough to warrant a different post on the blog. In the MRI case you have a human with macroscopic inhomogeneities, while in the spectroscopic case you are not interested in those macroscopic inhomogeneities, but in the local differences in molecules, that the active nuclei 'feel'. It's quite a difference in scale and also you have one human in the 'sample' in the case of MRI, but many molecules in case of spectroscopy :)