Speaking as a chemist who used to work with NMR (Nuclear Magnetic Resonance) and now works in healthcare administration, currently, NMR is the proper term referring to scientific research or the lab environment, while MRI (Magnetic Resonance Imaging) is the proper term referring to the imaging technology used in the healthcare environment. Although they share the basic underlying scientific principles, you cannot perform a MRI using a NMR and vice versa. I would hate to try and load a patient into the NMR spectrometer!

In the 'old' days, MRI was sometimes referred to as NMR or MRT (Magnetic Resonance Tomography), but if you use those terms nowadays instead of MRI, almost nobody will know what you are talking about.