Say I have a completely empty cylinder whose capacity is exactly 10 liters. It makes perfectly good sense to say that it will take 10 liters of a liquid to fill it. I don't get the gas part. If 1 gram of hydrogen is introduced into the cylinder, it will completely fill it because gases expand to fill whatever contains them. Exactly the same would happen if 10 grams of hydrogen had been introduced. How, then, can we say that some cylinder holds 3 liters of helium?

Remember that gas is compressible and in some cylinders, a lot of gas can be kept under pressure.

With gas, there is a pressure-volume relation. If you have some specific mass of gas, you can make it have any pressure you want, given it has a suitable volume.

For example, if you have 1 gram of Hydrogen in the cylinder, it will be under a pressure of 1.2 atm. With 10 grams of Hydrogen, the pressure of the gas would be 12 atm.

Now, for measuring and comparison purposes, some companies might bring the pressure to a constant and give the equivalent volume at that pressure.

Say for 1 atm, the first instant would be 12 L of Hydrogen gas and the second would be 120 L of Hydrogen gas, because, after all, when the gas is let out of the cylinder, that is in fact the volume the gas will occupy!
If they took 1000 atm, it would have been 0.012 L of Hydrogen gas and 0.12 L of Hydrogen gas in the cylinder.