I'm drafting information from my background in chemistry (university level) and a thorough read through my MD user manual. Excuse me in advance if i'm saying dubious hypothesis or if i am plainly wrong. Feel free to correct me.
The metal detector (at least mine) is made of 2 coils. The input coil and the detector coil. The central coil, also called the oscillator, generates a magnetic field which induce a current into the input coil. But the input coil is built on both sides of the oscillator, meaning that when one side tries to push electrons one way, the other side pushes them the other way, leaving a net signal (current) of 0.
When a piece of metal passes through the coil (or anything in fact), the magnetic field is changed, creating an imbalance between both sides of the input coil and generating a signal.
The nature of the metal (or any material) dictate how the magnetic field is deformed. On one side we got diamagnetic materials and the other we have paramagnetic material. Within the paramagnetic domain, we have some freaky behavior called Superparamagentism, ferromagnetism and ferrimagnetism. They all do the same thing as paramagnetism, just way stronger and, for some, longer.
When a paramangetic material is subjected to a magnetic field, it allows it to pass through while weakly strengtening it, the net effect is that it is attracted. It the reverse for diamagnetic materials, the generate a field of similar strenght but opposite direction, the net effect is that it is repulsed by the magnetic field.
Ferrous materials are either Ferrimagnetic or ferromagnetic, non ferrous are usually paramagnetic. Don't mind about superparamagnetism, it mostly happens with nanoparticles and i'd be surprised if you worked with those in the food industry.
Copper, silver, gold, aluminium, zinc, cadmium metals, for example, are diamagnetic, just like Carbon, Silicium, Nitrogen and the like
Now since the central coil that generate the magnetic field is connected to an oscillator, the field changes direction and goes back (a revolution) every determined interval of time (a frequency), usually this value is in Hertz (Hz) or per seconds. It follow a classic Sinusoidal wave.
Paramagnetic materials amplify the wave, increasing it height. Diamagnetic material, dampen or even cancel it. Both give a signal to the input coil, it is just different depending on where we are in time, compared to the oscillator wave, or the phase.
We can program the detector to look only of a portion of the sinusoidal wave, like the peaks of the wave that is at ±90°, or slightly around. Usually at 0°, there is no magnetic field. The angle of this portion is the phase.
But what does Stainless steel do in all this? it is clearly paramagnetic and should amplify the wave. Yes, it does...
But the phenomenon is not instantaneous. Good conductors like copper, aluminium or even iron react quickly to changes in the magnetic field. Stainless steel does not, it take close to half a revolution to react to changes.
This means that around 0°, there is a magnetic field that can be detected. This is why it is easier to detect Stainless steel at lower frequencies. This is also why, when testing the MD, we use stainless steel beads that are much bigger, more bulk means stronger magnetic field.
When we are looking for a phase around 0°, the signal is processed in a way that we negate the oscillator wave. Other metals can still be detected, since they are not exactly synchronised, but the dephased signal from SS is extremely clear.
Now you don't usually program your MD around what kind of metal you want to find, but around your product. You do not want to see the effect of your product in your detector.
Wet product tends to be good conductors and will interact with the magnetic field like most metals do. Low frequencies and a phase around 0° helps to ignore it.
Dry product are usually bad conductors and interact with the magnetic field like SS does. High frequencies and a phase around ±90° can cancel any effect it would have to the magnetic field.
Now i believe I've explained it all. I might go back and edit later if i find I lost myself in my explanations.