These Payment apps and Stripe are separate entities. Stripe is your payment gateway, and is in charge of processing transactions, making payouts and distributing refunds for your Stripe account.
Payment for Stripe is an avenue for collecting payments with your Stripe account, but is a 3rd-party and completely separate company. Here are additional key differences:
An extension to your Stripe account enabling mobile payments, invoicing and subscription management.
The infrastructure for creating payments and sending payouts to your bank account.