In Gift Card Account edit screen, why do we have both Redeemable and Active? What is the difference?
An active Gift Card is what you would expect - whether it can be used and applied to orders.
In Magento terms, 'Redeeming' a Gift Card gets applied to Store Credit. So disabling the ability to 'Redeem' a Gift Card forces a customer to directly use the code at checkout, instead of simply consuming it into Store Credit.
Interestingly (and annoyingly), the Gift Card module's ability to be redeemed (via System -> Configuration) does not drive the 'Redeem Gift Card' link in the Customer Dashboard, but rather whether Store Credit itself is enabled.
If you don't wish for customers to redeem cards to Store Credit at all, you'll need to either remove it from the template, or override
Enterprise_GiftCardAccount_Block_Account_Redeem to add an additional check to