What I am realizing is that some websites will log me out of PayPal after I pay for a purchase while other websites do not. Also, I realized that when I close my online banking window, my bank automatically logs me out of online banking. However, if I am in PayPal and close my PayPal window, I am not automatically logged out of PayPal. I can open a new window, go into PayPal, and I am still logged in.
What I am doing nowadays is *always* checking that I am logged out of PayPal.
Theoretically it is supposed to be much safer to pay with a credit card through PayPal, as PayPal adds an extra layer of protection. I don't think there's much protection, though, if you stay logged into your PayPal account long past when you think you left it.