Stripe only lets Administrators connect third-party apps like Payment for Stripe. So if several employees or volunteers use the app with their own Stripe logins, each one needs the Administrator role.
Payment Teams gives you more control over who uses the apps. With a Teams account you add staff logins instead. Staff take payments for your Stripe account, but they can't log in to Stripe, see your payouts, or use the Teams site. You choose which menus they see. Payments, Payouts, Invoices, Subscriptions, and Payment Links start hidden, and you can hide Customers and Coupons too.
Ready to set it up? See Teams plans compared (how to subscribe) and Add staff and set permissions.