Choose (or Buy) opens Paddle's overlay checkout on top of the page. For a logged-in customer, their email address is already filled in. Paddle asks for the rest (country, postcode, payment details, and a tax number for businesses), works out the tax, and takes the payment. Customers can enter a discount code there, unless Discount codes at checkout is off.

Everything inside the checkout is Paddle's. Its look is set in your Paddle account, under Checkout → Checkout settings.