Tuning is adjusting the radio frequency response of the NMR coils to minimize reflected power and put the radio frequency pulse to the sample. Pulses are usually under 50 Watts but reflected power is unwanted. A tuning "dip" is seen at the observe frequency when the probe is tuned to the sample. See the picture below:

The Varian Mercury 200 has a HX broadband probe, tuned to P

The Varian Mercury 300 has a HFCP probe that has both coils doubly tuned.

The Varian Mercury 400 has an ATB HCP probe that is insensitive to sample influence on tuning

The Varian VnmrS-400 has a AutoX automatically tuning probe

The Bruker AvanceIII 400 has an BBFOplus automatically tuning probe

The first two will be affected by sample, thus are a poor choice for samples with high dielectric or "saltiness".

The NMR sample is positioned in the coils of the NMR probe, thus the sample has a large effect on the tuning of the probe. The exception is the ATB probe, built by Varian, which is designed to limit sample effect on the tuning.

here is an empty probe, tuned:

Here is the same probe, with no change in the tuning capacitors, with a 200 mM NaCl(aq) sample inserted.

One can see that the tuning of the probe is greatly affected! Trying to observer P31 with this sample would be futile without re-tuning the probe. (as a side note, this was a saline sample from the teaching labs, there is no D2O or even any phosphorous compound in the tube, because the effect is simply an electric circuit effect involving capacitors, inductors and dielectric medium.)

Thus, even if the same nucleus is observed, samples can have large effects of the probe response. 

The new autotuning probes are very good in NMR because:

1. Users can have automatic access to a large number of nuclei, for example, Al27, Sn119, B11, P31 on the sample sample with no user intervention

2. The probes can be made more sensitive, with a higher Q, because the effects of the sample can be compensated