Do one cup of oil has the same mass as water?

The answer is NO.

One cup of oil does not have the same mass as water because they have different densities. Density is defined as mass per unit volume. Different substances have different densities, even if they occupy the same volume. In the case of oil and water, oil has a lower density than water. This means that for the same volume of oil and water, the oil will have less mass than the water. To put it simply, one cup of oil will weigh less than one cup of water, even though they occupy the same volume.