Donation forms and event registration forms can both use the Payment 2.0 part. This part allows users to pay for multiple transactions with a single charge.
If a user is logged in to BBIS and adds "Item A" to a shopping cart, then logs out of BBIS, "Item A" will no longer be in the shopping cart. If they add "Item B" as an anonymous user, and then log back in as an authorized BBIS user, "Item B" will no longer be in their cart. "Item A" will be back in their cart though. And if they log out again, "Item B" (but not "Item A") will be in the cart.
The cart associated with the logged-in user is a distinct cart from the one associated with the anonymous user. The cart will not be shared.
Website users who do not log in to your site can still add items to shopping carts.