PayPal Standard is an offsite payment method, so when your user selects that they are sent to PayPal, make a payment and then return back to the site.
PayPal Pro is an onsite payment method where your user enters their card details on your site, that info is sent to PayPal and they return success of fail, all whilst the user remains on the site…. however, onsite payment methods have a much higher scope for PCI compliance.
For PayPal standard you need just a normal PayPal business account, for PayPal Pro, you need a PayPal account that has website payments pro which incurs a monthly fee.
For lower PCI responsibility and no monthly fee I recommend using PayPal Standard, however which type of PayPal account do you have?