There are several different forms of PayPal. It sounds like you are using PayPal Standard, which always takes the visitor to PayPal’s website to process the payment.
There are a couple of different PayPal Pro type accounts where you can have the visitor fill out a single form, including their payment information if they are using a credit or debit card, and the form will both save to the WP database and process the payment with PayPal as the gateway. However, these accounts also require that you allow PayPal account checkout as a second option, in which case the visitor fills out the form on your website but when they submit the form they are taken to PayPal’s site to log in and complete the purchase. Since they are using a PayPal account, they just enter their email and password and don’t have to re-type their address or other details. These Pro accounts do come at a monthly fee – you might want to call PayPal to discuss your options. Being a nonprofit, they will give you a discount on the fees they charge to process payments.
I am not familiar enough with NinjaForms to know whether it integrates with these types of PayPal accounts. You might need to move to a different form system. Gravity Forms is one I know supports this type of payment, and I use it in the way described to receive donations and also capture the donors’ contact information.