I haven't used Store but have used Cartthrob, Membrr (as well as many other ecommerce engines) and wanted to add my thought.
You should have two sets of credentials - your live PayPal account details and your developer account details (sandbox). As far as I know these are completely separate - certainly in my experience I've just used two separate accounts.
You'll need to set up a buyer account in the sandbox that you'll use when you've proceeded to the PayPal payment page.
To test the cart while developing, obtain the API details from your sandbox account and add these to the PayPal gateway in the CP. Once you test the checkout process (I'm assuming this is for PayPal Standard/Express) you'll need to enter the sandbox buyer account details (see above) to test a payment.
As I said, haven't had experience of Store but this seems like a more general PayPal API question.