The integrate with PayPal's services you will notice there are three main channels (and IMO it's important to know this so you can decide the benefits for your application):
- IPN: Instant Payment Notification
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PDT: Payment Data Transfer
- PayPal's API
To use PayPal's IPN you need to add a 'listener' script (example) and add the address to your PayPal account. Whenever an event occurs PayPal will send a message directly to your server via your listener and you then update your accounts appropriately. This is especially useful for running subscription services as events will occur in the background without user intervention and you can capture successful/failed recurring payments etc.
PayPal's PDT is a system for accepting data when a user is redirected back to your site from PayPal. For example, a user clicks 'Buy', they are directed to PayPal, enter information etc. Then, once the payment has been taken, they are redirected back to your site. PayPal can pass details about the transaction including whether it was successful or not so you can display the appropriate success/failed page from your site.
PayPal's API allows you to integrate more deeply with PayPal's services, and you would use this if you were managing payments directly from your site.
These services aren't mutually exclusive, so you can use any combination with your application.
I hope this helps