If gases occupy all the volume in a container then how can we define 'volume percent' as all different gases will have same volume?
We can and do use volume fractions to express the level of a gas of vapour in air, it is volume ppm. For example air to a first approximation is 20 % oxygen and 80 % nitrogen.
This means 20 % of the molecules in air are oxygen while 80 % are nitrogen. If we treat the gases as ideal gases then air is by volume 20 % oxygen.
The point you have to remember about ideal gases (and gases at atmospheric pressure a a good approximation of ideal gases) is that the particles of the gas don't interact. This applies to mixtures as well as pure gases.
So, in one sense, if you fill a vessel with a mixture of gases, each does occupy the whole vessel. But the gases are also perfectly mixed as they don't separate out. If you calculated the pressure for a fixed amount of each gas separately in a vessel of a given size, then the answer you would get would be the partial pressure of the gas in a mixture containing the same amount of the specific gas.
As an alternative, if you kept the pressure fixed and calculated the volume occupied by the gas, the volume would be proportional to the amount of the gas. The volume of the components would add up the total volume of the vessel containing the mixture at the same pressure. This means that the volume % is proportional to the amount of gas molecules in the mixture and to the partial pressures. Volume and partial pressure are proportional for ideal gases so volume %, partial pressure and mole % are the same.