Are Visa and Mastercard owned by the same company?

Nope. They are competitors. They are two separate entities, with both VISA and Mastercard being American companies, (and they are also listed as VISA and Mastercard respectively outside the US as well). The reason why they are both mentioned in the same name comes from the fact that they operate in almost all the countries of the world. If a Bank is not working with VISA, then it is working with Mastercard and vice versa. Nowadays, many banks opt to work with both.

The naming of both VISA and Mastercard in the same sentence comes from the POS terminals industry salesmen, where the POS network operators had a great advantage in selling/leasing out POS machines that would capture and do transactions on both VISA and Mastercard, hence the terminology stayed from an acceptance point of view VISA/Mastercard.