The option to accept credit card payment through your Paypal standard account is well hidden in the Paypal setup settings.
Locate My Business Setup > Customise my buyer's experienceLocate the Auto return
Locate Website Payment Preferences
Locate PayPal Account Optional
Click to switch this feature ON.
When this feature is turned on, your customers will go through an optimized checkout experience. This feature is available for Buy Now, Donations, and Shopping Cart buttons, but not for Subscription buttons.
But it is not that straight forward as Paypal explains further down:
When PayPal Account Optional is turned on, your customers who are new to PayPal will no longer be required to create a PayPal account to complete a purchase—they will go through an alternate checkout, and will have the option to sign up afterward. Customers who already have PayPal accounts will continue to enjoy the privileges of those accounts, such as payment history and integration with eBay Auctions, and their checkout experience will remain the same.
This feature is available for Buy Now, Donations, and Shopping Cart buttons, but not for Subscription buttons.
Note: If you have turned on Auto Return and have chosen to turn on PayPal Account Optional for new users, a new user will not be automatically directed back to your website, but will be given the option to return.
It looks like Paypal tries to detect if a client has already a Paypal account and in this case will force them to use their Paypal account. In our experience, you may need to complain to the Paypal technical support to have this option displayed.