Two liquids that have the same volume don't necessarily have the same density. Density = mass/volume, so they would only have the same density if they also have the same mass.
Density is an intensive property, which means that it doesn't depend on the amount of the substance present. If two liquids have the same density, then any volume of the first substance will have the same density as any volume of the second substance. Changing the volume of a substance doesn't change the density.
As an example, mercury is a liquid metal whose density is 13.5 times that of water. If you have 10 ml of mercury and 10 ml of water, the mercury will have a mass of about 135g and the water will have a mass of 10g, so mass/volume of the mercury is greater than that of water and mercury therefore has a higher density. This would be true for any equal volume of the two substances.