In the bottom-right corner of credit cards, you'll find the logo of a payment company such as Visa, Mastercard, or TROY. (On debit cards, you'll instead see Visa Electron or Maestro.)
So what do these logos mean?
Their overall purpose is actually the same: to move the cash flow that exists in the world onto systems such as debit cards, credit cards, and prepaid cards. Even today, around 80% of the world still uses cash.
Visa and Mastercard are two competing companies that specialize in payment systems. (In 2016, Turkey launched its own scheme, TROY -- short for "Turkiye'nin Odeme Yontemi," or "Turkey's Payment Method.") For the user, there is no real difference between them. The difference only shows up operationally, through the agreements banks make with each scheme. In practice, you deal with your bank for all of your spending; your bank, in turn, deals with Visa or Mastercard because it uses their infrastructure.
When banks launch a new product, they first decide which brand it will be issued under. They then request a new BIN (the first 6 digits of the card) for that product from the scheme. Once the required fees and certifications are completed, the BIN is registered in that company's system (Mastercard, Visa, or BKM). This is what allows the resulting cards to be used abroad without any issues.