I have a multimeter adjusted in DC tension mode. When I put my two wire connections inside a water container, I measure +120 mV or sometthing less but never zero. Why do I measure a potential difference ?
This is common, and is because the two probes aren't exactly of the same metal. They may have started out that way, but over time each was exposed to a different history of corrosion, sweaty fingers, and the like. The result is that the two probes no longer have exactly the same electro-chemical potential.
Put another way, each probe in the water is acting like half a battery. Since they aren't identical, they don't produce exactly the same voltage. The difference between the two half-battery potentials is what the meter is showing you.
Instead of one of the probes directly in the water, try a different metal and connect the probe to that metal out of the water. That should give a larger difference between the probes. You can also try other conductive substances, like a graphite rod.