When you download an app on Google Play, it uses the Google payment system by default. Even if the actual payment is made via PayPal, SMS, or any other payment method, it is registered in the Google system either way, and there is no way to bypass this.
When you register on Google Play, a similar account on payments.google.com is created automatically. This account contains the information about all the purchases you make. Your Gmail address serves as a login, while your password matches the one for your Google account.