If you want to open an account on PayPal, you need to have email address you can confirm. Your PayPal account will be linked to your bank account or your credit card you will be using for financial operations. However, when you make a deposit, an online casino will only see your email address without any other personal information you might not wish to reveal.
Vice versa, when you make payments via your account in the traditional bank, the receiver usually sees your personal information such as name, address of residence, details of your bank account. From this point of view, paying using PayPal is more anonymous and safer, as nobody can steal your personal data.