Customer sessions stores data related to customer, checkout session stores data related to quote and order. They are actuall under one session in an array. So firstname in customer/session will be $_SESSION[‘customer’][‘firstname’] and cart items count in checkout/session will be $_SESSION[‘checkout’][‘items_count’]. The reason Magento uses session types separately is because once the order gets placed, the checkout session data information should get flushed which can be easily done by just unsetting $_SESSION[‘checkout’] session variable. So that the session is not cleared, just session data containing checkout information is cleared and rest all the session types are still intact.